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Inverse of a function (Gr 12 math)

  1. Sep 20, 2009 #1
    Inverse of a function.. (Gr 12 math) [SOLVED]

    1. The problem statement, all variables and given/known data
    If point (a,b) is on the line of y = f(x), what poin must be on the line of:

    1. y = [tex] f\left(-\frac{1}{2}x\right)+1 [/tex]
    2. *Trouble question* [tex] y=f^{-1}(x)+2[/tex]


    2. Relevant equations



    3. The attempt at a solution

    My answer for the first was : [tex]\left(-\frac{1}{2}a, b+2\right)[/tex]

    the second one bothers me... i know you have to swap the domain and range. but normally the questions i get are if y = 2x + 3, what is the inverse of the function. I then swap the x and y to get x = 2y + 3 then rearrange to end up with the answer y= (x-3)/2 but i dont really know where to start here...

    I don't have an answer key for this worksheet. but what do i do, do i just go x = y +2 and do the reverse, then i would answer (a-2, b+2)? This is really bugging me.

    Regards,
    Senjai
     
    Last edited: Sep 20, 2009
  2. jcsd
  3. Sep 21, 2009 #2

    HallsofIvy

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    Re: Inverse of a function.. (Gr 12 math) [SOLVED]

    No. You are completely misunderstanding the point of the problem. All you know about f is that f(a)= b so to be able to find f((1/2)x) at all, you must have (1/2)x= a. Now what is x? And, since f((1/2)x)= f(a)= b, what is y?

    What happened to f? This has nothing at all to do with "x=y+2" or "y= x=- 2".
    Since all you know about f is that f(a)= b, all you know about f-1 is that f-1(b)= a. So in order to say anything at all about f-1(x), you must have x= b. In that case, f-1(x)= f-1(b)= a. So what is f-1(x)+ 2.

    Notice that in neither of these questions are you asked anything very general- just to determine a single point on the graph.

     
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