Thread: Finding the rate of change of an inverse function given certain values

Hi,

The problem says:

For a function f it is given that
f'(7)= -4 f^-1(7)= -3
f'(-3)= 12 f^-1(-3)=8

Find the rate of change of f^-1(x) at x=7.

I have been trying to solve this problem, but I am getting very confused so I am getting nowhere. I would really appreciate it if anyone could give me a hand. Thanks!

I know this so far, but I think I haven't got it right...

f(f^-1(x))=x. Let y=f^-1(x), then f(y)=x.

So (df/dy)*(dy/dx)=1 --> dy/dx=1/(df/dy) --> dy/dx=1/(f'(-3)) as f^-1(7)=-3. So dy/dx=1/12

You have that exactly right. What makes you think otherwise?

Thanks a lot! I'd asked someone in my class and he said he thought it was wrong...but I'm glad he was wrong. I am kind of new to this so I wasn't sure.

Thanks for your help!