# How do you find the inverse of #f(x) = x / (x + 8)#?

Let

#f^(-1)(y) = (8y)/(1-y)#

So:

So:

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To find the inverse of the function ( f(x) = \frac{x}{x + 8} ), follow these steps:

- Begin by swapping the roles of ( x ) and ( y ), so the function becomes ( y = \frac{x}{x + 8} ).
- Next, solve this equation for ( x ) in terms of ( y ).
- Swap ( y ) and ( x ) back to get the inverse function.

So, let's start with ( y = \frac{x}{x + 8} ).

Step 1: Swap ( x ) and ( y ): [ x = \frac{y}{y + 8} ]

Step 2: Solve for ( y ): [ x(y + 8) = y ] [ xy + 8x = y ] [ xy - y = -8x ] [ y(x - 1) = -8x ] [ y = \frac{-8x}{x - 1} ]

Step 3: Swap ( y ) and ( x ) back to get the inverse function: [ f^{-1}(x) = \frac{-8x}{x - 1} ]

So, the inverse function of ( f(x) = \frac{x}{x + 8} ) is ( f^{-1}(x) = \frac{-8x}{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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