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opus

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## Homework Statement

For ##y=f(x)##,

find the slope of the tangent line to its inverse function ##f^{-1}## at the indicated point P.

##f(x) = -x^3-x+2## , ##P(-8,2)##

## Homework Equations

The Inverse Function Theorem:

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

## The Attempt at a Solution

So I'm stuck at square one. I need to find the inverse of ##f## and am having troubles doing so.

The given is ##f(x) = -x^3-x+2## and I'm at a stand-still in isolating the x.

##f(x) = -x^3-x+2##

##y = -x^3-x+2##

##y-2 = -x^3-x##

##y-2 = -x(x^2+1)##

.

.

?

Could someone poke my brain a little on this one?