# How do you find the inverse of #g(x) = y = (x-6)^5#?

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To find the inverse of the function ( g(x) = (x - 6)^5 ), follow these steps:

- Replace ( g(x) ) with ( y ).
- Swap the variables ( x ) and ( y ).
- Solve the resulting equation for ( y ).
- Replace ( y ) with ( g^{-1}(x) ) to express the inverse function.

Let's proceed with these steps:

- Start with ( g(x) = (x - 6)^5 ).
- Replace ( g(x) ) with ( y ) to get ( y = (x - 6)^5 ).
- Swap ( x ) and ( y ) to get ( x = (y - 6)^5 ).
- Solve for ( y ): [ x = (y - 6)^5 ] [ \sqrt[5]{x} = y - 6 ] [ y = \sqrt[5]{x} + 6 ]

So, the inverse function of ( g(x) ) is: [ g^{-1}(x) = \sqrt[5]{x} + 6 ]

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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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