# How do you find the inverse function of #f(x) = (2x-3)/(x+4)#?

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To find the inverse function of ( f(x) = \frac{2x-3}{x+4} ):

- Replace ( f(x) ) with ( y ).
- Swap ( x ) and ( y ) to obtain ( x = \frac{2y - 3}{y + 4} ).
- Solve this equation for ( y ).
- First, multiply both sides by ( y + 4 ) to eliminate the denominator.
- Then, distribute to get ( x(y + 4) = 2y - 3 ).
- Expand: ( xy + 4x = 2y - 3 ).
- Rearrange terms: ( xy - 2y = -4x - 3 ).
- Factor out ( y ): ( y(x - 2) = -4x - 3 ).
- Divide both sides by ( x - 2 ): ( y = \frac{-4x - 3}{x - 2} ).
- Replace ( y ) with ( f^{-1}(x) ) to get the inverse function.

Therefore, the inverse function is ( f^{-1}(x) = \frac{-4x - 3}{x - 2} ).

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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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