Question

Suppose f^-1 is the inverse function of a differentiable function f and f(4) = 6, f'(4) = 5/7 then f(-1)'(6) = ?

Answer 1

\[(f^{-1})'(x)=\frac{1}{f'(f^{-1}(x))}\]

Answer 2

how do i find the derivitive of that without the equation?

Answer 3

you don't need it, you are just asked for the value

Answer 4

here is what you need:
\[f(4)=6\]which tells you \[f^{-1}(6)=4\]

Answer 5

actually you do need one more piece of information, don't you? you need \(f'(4)\)

Answer 6

where you told that somewhere in the problem?

Answer 7

No i was not.
That is an exact copy of the problem

Answer 8

sorry i fogot the f^-1 part. i dont know if that makes a differnce for solving though

Answer 9

then there is some mistake here
there are an infinite number of functions with \(f(4)=6\) you need \(f'(4)\) as well

Answer 10

no you need \(f'\) evaluated at the number also

Answer 11

oh wow. my bad. completly missed this part. i will update the question

Answer 12

i believe you, there just must be some mistake here

Answer 13

anyway, whatever it is, it is just the reciprocal

Answer 14

no i overlooked that somehow when i was typing
but the updates should be made

Answer 15

ok I see that now. Sorry for all of the confusion thanks for helping me. :)

Answer 16

here is the formula that always works
\[(f^{-1})'(x)=\frac{1}{f'(f^{-1}(x))}\]

Answer 17

yw