1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.

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


    User Avatar
    Science Advisor

    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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook