# What is the inverse of #f(x) = (x+1)/(2x+1)#?

Take the reciprocal of both sides to get:

So

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To find the inverse of ( f(x) = \frac{x+1}{2x+1} ), follow these steps:

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

Starting with ( y = \frac{x+1}{2x+1} ):

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

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

[ 2xy + x = y + 1 ]

[ 2xy - y = 1 - x ]

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

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

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