# How do you find the inverse of #f(x)=(2x+7)/(3x-1)#?

Let

Eliminate all but one of the

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To find the inverse of the function ( f(x) = \frac{2x + 7}{3x - 1} ), follow these steps:

- Replace ( f(x) ) with ( y ).
- Swap the roles of ( x ) and ( y ): Rewrite the equation as ( x = \frac{2y + 7}{3y - 1} ).
- Solve this equation for ( y ).
- Once you have ( y ) expressed in terms of ( x ), replace ( y ) with ( f^{-1}(x) ) to denote the inverse function.

Let's go through the steps:

- Original function: ( f(x) = \frac{2x + 7}{3x - 1} )
- Swap roles of ( x ) and ( y ): ( x = \frac{2y + 7}{3y - 1} )
- Solve for ( y ): [ x(3y - 1) = 2y + 7 \ 3xy - x = 2y + 7 \ 3xy - 2y = x + 7 \ y(3x - 2) = x + 7 \ y = \frac{x + 7}{3x - 2} ]
- So, the inverse function is ( f^{-1}(x) = \frac{x + 7}{3x - 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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