# If g is the inverse of f and if #f(x)=x^3-5x^2+2x-1#, how do you calculate g'(-9) if the domain of f(x) is the set of integers less than 0? Thanks in advance for taking time to help me out. Steve?

Use

Should you possess knowledge of the rational zeros theorem, apply it. If not, utilize "by inspection"—a fancy term for "guess and check"—to solve the problem.

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To find ( g'(-9) ), first, we need to find the inverse function ( g(x) ) of ( f(x) ). Then, we evaluate the derivative of ( g(x) ) at ( x = -9 ).

Given ( f(x) = x^3 - 5x^2 + 2x - 1 ), to find the inverse function:

- Let ( y = f(x) ).
- Swap ( x ) and ( y ): ( x = y^3 - 5y^2 + 2y - 1 ).
- Solve for ( y ).

After finding the inverse function ( g(x) ), differentiate it to find ( g'(x) ), and then evaluate ( g'(-9) ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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