Full transcript of “GRAPHS OF INVERSE FUNCTIONS || GRADE 11 GENERAL MATHEMATICS Q1”. Click a timestamp to open the video at that moment. Need another video? Use the YouTube transcript generator.
0:03 [Music] Hika Walmart's we discuss going on I about graphs of inverse function dropping inverse function so given the graph of a one-to-one function the graph of its inverse can be obtained by reflecting the graph about the line is equal to X so Miss mcgoun then the gamma turnitin an application of any cropping up like for example the decimals but must map Adela is saying you to graph the inverse function at Makita new reflection new original function again
0:50 this is the continuation of the inverse of one to one function for example number one crap y is equal to the inverse of f of X if the graph of the original function is equal to 2x plus 1 restricted in the domain so your X should be greater than or equal to negative 2 but less than or equal to 1.5 so that will be your graph so my restriction again negative 2 long and up to 1.5 what is the range of f of X what is the domain and range of its inverse so a non gagawin you first is graph the
1:40 original function so this is y is equal to 2x plus 1 so prom negative 2 2 so this the X bar is now negative 2 to 1.5 so it is from 1.5 now what will be the value of range since that is why no thank etang in a minor you know why not in apps to positive 4 and this will be here okay so what will be the range in inverse or the domain and what is the dominant range of its inverse okay next slide tire take the reflection of the
2:28 restricted graph y is equal to 2x plus 1 across the line y is equal to X the range of the original can be determined by the inspection of the graph Madalena telegram identify must smother leme identify a range kiseki tanky tenements a graph ok so again now who had nothing arranged by observing the graph so with the hiss of this graph running emerging range nothing so of course the Teen Titans oye since honking positive for sha so your Y value should
3:13 be greater than or equal to 4 oh no should be 3 no well that's a negative 3 up to positive 4 so your Y is greater than or equal to negative 3 but less than or equal to positive 4 so genuine America title Detroit Eaton's your Incheon to see you doming and detour detour eating is a x-axis near ok now good not were napping and dominantly in sting and not in your reflection yeah okay if only you knew original function
3:59 so hopper dinamita not in the rest dismiss or grab motika or any kinds of graph application this will be the inverse of 2 X plus 1 so it will not a red line now using the using this one that are yeah the graph of the inverse of 2 X plus 1 a new denying on value no domain yes empathy being led to sex amadito so Malati negative 3 Hangang capacity for pignon Omega so on X values mana on you don't mean mine eyes X is greater than or equal to
4:46 negative 3 but less than or equal to 4 at a range mana would love a negative 2 and positive 4 so under no observed no sir grapple say inverse no graph not in Marin behind observe so my observing a class you know mean little original function I Ranger Ranger none inverse function on graph no inverse function tapas young range no original function I don't mean the man inverse no original
5:33 function so he big Sabine class like interchange lung in position and domain of original function range shannon inverse function young range now original function domain china inverse function no ha hey sorry now observe ian so that is the value of range know a set of all real numbers but your X is or your Y no opposite a range is from negative 3 to positive 4 of verify using techniques in getting the inverse getting the inverse of the function we
6:21 come up this inverse function or so the original function is 2x plus 1 so capadino are nothing inverse Virginia Maggie Ginn can eat all so third party teen an Athenian ok this will know the summary canina so original andö mania is set of all real numbers but your X is greater than or equal to negative 2 but less than or equal to 1.5 but that inverse function shown the Union range aha so that interchange lancia young range the original function in range natum i domina
7:07 d Tosa inverse function sannen desu son daniel on a pseudonym discussion attend next observe that the domain of the inverse is the range of the original function and that the range function f of the inverse is the domain of the original function is this true for all one-to-one function in der inverses thinking that is a pinion etiqueta is this true for all one-to-one function in their inverses let's try more examples now find inverse or function 1 over X or
7:55 f of X is equal to 1 over X using each given graph ok so using any application this is the graph of 1 over X applying the horizontal line test we verify that the function is one-to-one yes so kites unknown again it has here the horizontal line well I'm taught a man Janet 11.9 graph so therefore this graph is a one-to-one function since the graph of f of X is equal to 1 over X is symmetric with respect to the line y is equal to X indicated by a dashed line its reflection across the line y is
8:43 equal to X is itself a big Sabine class u inverse neato I am sorry linear in ha so therefore the domain and range are the same okay Cassie class using the previous discussion how to get the inverse function ok debug an interchange meal X can see so mu Y in terms of X so making X is equal to Y over Y so so glue n cy x over y is equal to 1 so divide both sides by X also good for any one over X so in this example number two the
9:30 inverse of 1 over X is also 1 over X / a Aslan Silla now what next find the inverse of f of X is equal to cube root of x plus 1 using the given graph what do you think this is a one-to-one function or not that is a one-to-one function C's Punkie knoweth nothing yeah no that is tree using the given graph ok we are going to get the inverse of the f of X is equal to cube root of x plus 1
10:17 okay ting in a pen this is the original function you'll knock a black little black in color in and grab and this now the inverse so using the previous discussion you come up the inverse of this so but now Ohanyan now this is the graph the result of the reflection of the graph of f of X is equal to the cube root of x plus 1 is the graph of y is equal to X cubed minus 1 therefore the inverse of f of X is equal to X cubed minus 1 so it'll never end at all that is X cubed minus 1 z
11:05 inverse little cube root of x plus one okay again this is a one-to-one function for example number four I'll give you an example of rational function okay f of X is equal to 5x minus 1 all over negative x plus 2 this is the graph of the given rational function find its domain in range given the rational function so partying at my in domain and range okay the by in domain I think you know who I not in Dulce denominator Kalin MacEwan
11:52 attention value 9x Mahua not inversion and ixnay hindi depatment equal to 0 so therefore equate nothing in denominator not insincere also negative x plus 2 equals 0 LeapPad c+ 2 Sahab Allah so let me John so mugging negative x equals negative 2 a negative index not and multiply both side by negative one so you'll X naught n is positive 2 okay now the pad now you'll X not in detail hindi pretty mug in positive 2 so anima given domain attend a set of all real numbers except positive 2 hahaha you arrange numb and
12:39 palutena will arrange our rational function teen eating an Athenian degree of polynomials the numerator and denominator kappahd equal and degree of polynomials the numerator and denominator nothing CAG Anita the degree of polynomial in numerator is 1 that's the exponent the trains denominator is 1 equal Silla kappa equal Silla how to get the range divide new lon yo numerator and denominator you numerical coefficient in learning numerical coefficients numerator 5 denominator negative one so you know needy divided you apart equal and degree
13:26 of polynomial so 5 divided tentative 1 so therefore your range range is all set of real numbers but Y is not equal to negative 5 so again going back to the definition how to find the domain and range of the inverse function so third poor young range net or animal a anomaly inverse you know minima you arrange NATO Shyam domain and inverse - neato a kendama in a mansion when you arranged on inverse another is to find a the
14:12 asymptotes or the equation of its asymptotes so paddle back in Hawaii asymptotes medal along the man comes a new restricted come on every strict it's a domain and range Union vertical and horizontal asymptotes Teeter said don't mean I know restrict Edna X values day but to say der for your vertical asymptotes that is X is equal to two syringe and you restricted version and Y negative five so therefore you horizontal asymptotes not in his negative five so that one X is equal to positive 2 and Y is equal to negative pipe again keno who are not into running
14:57 restricted values a domain in range another example okay by the way here you know the reflection or the inverse graph of the original function so he to read that is the inverse function okay so how does seems on you and Anila you presto like movement on Radner so observe that the new asymptotes are the old asymptotes with the x and y values interchange the asymptotes could also be obtained by reflecting the original asymptotes about the line y is equal to X so therefore the vertical asymptotes
15:45 now at a yawn with your only time a broken line is negative five and the horizontal asymptote is positive three this one this is for the inverse function ax pelo Kapaa original function your vertical asymptotes nothing is positive two and then the horizontal asymptote is negative five so the interchange learned impressed or you are not in your original function inverse function okay now so this is the summary no Sidonie no original function all set of all these numbers but except positive
16:32 two syringe newman original function all the ill numbers except negative five neaten a man like palette lovin impressed off okay like palette lancelin impressed or it all so c domain again green C inverse C range so original function again dominum inverse function okay sign Anderson Dan let's proceed for the problem solving so Marin a handle on problem solving data you as a friend pink urban and negative numbers add two to the number square the number multiply the result by 3 and divide the result by 2 if the result is 54 what is the
17:20 original number construct an inverse function that will be provided or regional number that is salt is given okay and wound in the patent and a understand money in problem a nobleman adapt at nothing teen answer problem okay so maybe negation Direction corneum Gago and in them if the result is 54 haha not be nineteen what is the original number using the inverse function okay DNA I will pink any non-negative numbers or I will represent it as X add two to the numbers so this add to the number square
18:06 the number so this one sphere multiplied by 3 and divide by 2 so about a nice not end Paragon it again 3x plus 3 times X plus 2 squared over 2 that is the original function the graph is shown below on the left now below yes this one this is not a one-to-one function because they grabbed this netsertive satisfy the horizontal line test however the instruction indicated that the number the original number must be non-negative the original of the function must thus be restricted to X is greater than or equal to 0 and it's graph is shown on
18:53 the right below so it 839 you know so the function with a strict a domain X is greater than or equal to 0 is then I want to one function and we can't find it in words interchange the X and y variables so using the how to find the inverse function okay from here we interchange Y as X naught 3 times y plus 2 squared over 2 so that will become cross multiplication 2 times X 2 X is
19:41 equal to 3 y plus 6 over 2 or 3 a y plus 2 over 2 so divide both side by 3 that will be y plus 2 squared is equal to 2x over 3 since Y is greater than or equal to 2 we do not need we do not need to consider negative corrects Cassie greater than or equal again so bowel share so therefore the inverse function must be the square root of 2x over 3 minus 2 okay therefore so let's evaluate the function if your ex
20:28 is 54 so the answer will be positive 4 so your original number now is 4 so you checking in at in bossy deetle deetle teaching at indy tone doing so directional okay cool for yong-ok comporting and I think Aldama inside goodnight angle 54 4 plus 2 6 is squared nothing in 636 multiply the result by 3 so 36 bar times 3 what is the answer
21:14 36 times 3 so that is 108 8 Dominick I said 3 6 times it ok 108 divided by 2 that is pitiful okay correct so the original number is 54 using the inverse function we know to volunteer next ok this problem engineers have determined that the maximum force TN tones that a particular breed skincare is related to the distance D in meters between its
22:00 supports by the following function T of D is equal to 12.5 over T to the third power how far should supports be if the breeds is to support 6.5 tones per stock and inverse function to determine the result okay so the equation is this T is equal to 12.5 over D raised to 3 the lesson confusion in this case let us not interchange bnps d denoted specific values salt instead for D in terms of T ok so I'll am dominar then so the cube root of T is equal to 12.5 over D so
22:49 therefore B is equal to 12.5 times 12 point 5 over the square root of P the equation of the function so we are going to evaluate six point five so therefore that is 6.70 the support should be placed at most six point 70 meters apart now meet the inverse function they put the practice exercises in proposing a talk about directly nationa okay I'll give you one minute a picture I know well you Munna has e next notice in
23:37 under the next slide Nieto you cigar when you try to answer it for number one f of X is equal to the square root of four minus X is restricted on the domain X is set of all real numbers but your X is greater than or equal to negative five but less than three what is the domain of its inverse given the graph of F of X is equal to the square root of 4 minus X below sketch the graph of its inverse so pedagogy monitoring their s'mores using algebraic methods construct the universe of f of X is equal to 4 or is equal to the square root of 4 minus X is the function you
24:22 get the same as the sketch of inverse in the previous number okay this will be the answer for number one and for number two the domain of the inverse of f of X is just the range of f of X such that the range of f of X is y or y is greater than 1 but less than or equal to 3 but therefore the domain in the inverse is X is greater than 1 but less than or equal to 3 in the solution for the practice exercises number 2 this the graph is the inverse of the original graph and for
25:08 practice exercises number 3 so we're using this given function and we follow the steps in getting the inverse of this function so therefore the inverse is 4 minus x squared so ever the graph of that elicits a result a parabola so therefore the practice exercises number 3 is not a one-to-one it fails on the result align test ok that's all for the graphic of inverse function see guramukh gaga upon it come in another video for that but i must maintain the any path
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