# How do you find the inverse of #f(x) = (x - 2) /( x + 2)#?

Let

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To find the inverse of the function ( f(x) = \frac{x - 2}{x + 2} ), follow these steps:

- Replace ( f(x) ) with ( y ).
- Swap ( x ) and ( y ): ( x = \frac{y - 2}{y + 2} ).
- Solve this equation for ( y ).
- Once you have ( y ) in terms of ( x ), replace ( y ) with ( f^{-1}(x) ) to get the inverse function.

Solving step 2 equation for ( y ), we get:

[ x(y + 2) = y - 2 ]

[ xy + 2x = y - 2 ]

[ xy - y = -2x - 2 ]

[ y(x - 1) = -2(x + 1) ]

[ y = \frac{-2(x + 1)}{x - 1} ]

So, the inverse function is ( f^{-1}(x) = \frac{-2(x + 1)}{x - 1} ).

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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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