Question

Let f be differentiable such that f(-2)=3,f(3)=5, f'(-2)=4 and f'(3)=6. Let g be differentiable functions such that g(x)=f^-1 (x) for all x. What is the value of g'(3)

Answer 1

`g'(3)=(1)/(4)`

Explanation:

There is a rule in calculus that tells us that:

`g'[f(x)]=(1)/(f'(x))`

In this case, we know that f(-2)=3, therefore:

g'(3)=g'(f(-2))

So, if we used the rule, we would get that:

`g'[f(-2)]=(1)/(f'(-2))`

we know that f'(-2)=4, so:

`g'[f(-2)]=(1)/(4)`

or:

`g'[3]=(1)/(4)`