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## Homework Statement

If f(x)=x^3-x-6 and g is the inverse function of f.

what is f'(g(0))g'(0)?

the answer is 1...but im not sure how to get that.

## Homework Equations

[f(g(x))]'=f'g(x)*g'(x)

## The Attempt at a Solution

i wasnt quite sure, but i assumed g(x)=1/(x^3-x-6)

^is this assumption right?

then f'(x)=3x^2-1

i also set f(x)=0 to find x=2.

but for g(0) i get -1/6

so for f'(g(0))g'(0)= i get -1(-1/6)*(-1) = -1/6

but this is incorrect.