## anonymous 4 years ago Find ( f -1 )'( a )

1. anonymous

2. anonymous

f^-1*

3. anonymous

ok you are in luck because $f(1)=5$ so $f^{-1}(5)=1$

4. anonymous

What does the apostrophe mean?

5. anonymous

you want $f^{-1^'}(5)$ and you do that by finding $\frac{1}{f'(f^{-1}(5))}$

6. anonymous

fortunately you know $f^{-1}(5)=1$ so this becomes $\frac{1}{f'(1)}$ therefore your actual job is to take the derivative, evaluate it at 1, and then take the reciprocal.

7. anonymous

Ok, sorry I'm slow on this, I'm taking some tests to get ready for college. I'm going to try and work this backwards, they give my 5 answers. I believe that the correct answer is 5/3?

8. anonymous

i really didn't do it. whatever the derivative is, evaluate at 1 and flip. i can check if you want

9. anonymous

yeah you got it! $\frac{5}{3}$