# Given #f(x)= x^3 +2x -1#, how do you find #1/ [f^(-1)(2)]#?

and so:

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To find ( \frac{1}{f^{-1}(2)} ), follow these steps:

- Determine the inverse function of ( f(x) ), denoted as ( f^{-1}(x) ).
- Once you find ( f^{-1}(x) ), evaluate ( f^{-1}(2) ).
- Then, calculate ( \frac{1}{f^{-1}(2)} ).

Here's the detailed process:

- Start with the given function: ( f(x) = x^3 + 2x - 1 ).
- To find the inverse function ( f^{-1}(x) ), swap ( x ) and ( y ) in the equation and solve for ( y ).
- So, ( x = y^3 + 2y - 1 ).
- Rearrange this equation to solve for ( y ).
- Once you find ( f^{-1}(x) ), plug in ( x = 2 ) to find ( f^{-1}(2) ).
- Finally, calculate ( \frac{1}{f^{-1}(2)} ).

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To find (\frac{1}{f^{-1}(2)}), first find the inverse function of (f(x) = x^3 + 2x - 1), denoted as (f^{-1}(x)). Then, substitute (2) into the inverse function and take the reciprocal of the result.

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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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