# How do you find the inverse of #f(x)=x^3-2# and is it a function?

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To find the inverse of ( f(x) = x^3 - 2 ) and determine if it is a function, follow these steps:

- Replace ( f(x) ) with ( y ).
- Swap the roles of ( x ) and ( y ).
- Solve the resulting equation for ( y ).
- Replace ( y ) with ( f^{-1}(x) ) to express the inverse function.
- Check if the inverse function passes the vertical line test to determine if it is a function.

Here are the steps applied to ( f(x) = x^3 - 2 ):

- Replace ( f(x) ) with ( y ): ( y = x^3 - 2 )
- Swap the roles of ( x ) and ( y ): ( x = y^3 - 2 )
- Solve for ( y ): [ x + 2 = y^3 ] [ y = \sqrt[3]{x + 2} ]
- Replace ( y ) with ( f^{-1}(x) ): [ f^{-1}(x) = \sqrt[3]{x + 2} ]
- To determine if it is a function, check if the inverse passes the vertical line test. Since the cube root function is a one-to-one function (each input has a unique output), the inverse ( f^{-1}(x) = \sqrt[3]{x + 2} ) is also a function.

Therefore, the inverse of ( f(x) = x^3 - 2 ) is ( f^{-1}(x) = \sqrt[3]{x + 2} ), and it is a function.

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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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