Question

Suppose g(x) = the inverse of f(x). If f (2) = 3 and f '(2) = 7, find g'(3).

Answer 1

Formula:
\[\Large\bf\sf \frac{d}{dx}f^{-1}(x)\quad=\quad \frac{1}{f'\left[f^{-1}(x)\right]}\]Since g is our inverse,\[\Large\bf\sf \frac{d}{dx}g(x)\quad=\quad \frac{1}{f'\left[g(x)\right]}\]And then we just need to plug some stuff in.

f(2)=3 implies that g(3)=2, right?
Since they're inverses.\[\Large\bf\sf g'(3)\quad=\quad \frac{1}{f'\left[g(3)\right]}\]

Answer 2

I get it! Thank you, it was a lot easier than I thought.

Answer 3

Ya not too bad :)
Just need to remember that weird formula for inverse derivatives.