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

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

- Replace ( f(x) ) with ( y ).
- Swap ( x ) and ( y ) to get ( x = \frac{{2y - 1}}{{y - 1}} ).
- Solve this equation for ( y ).
- Multiply both sides by ( y - 1 ) to get rid of the denominator.
- Simplify the equation and solve for ( y ).
- After finding ( y ), replace it with ( f^{-1}(x) ) to get the inverse function.

The inverse function ( f^{-1}(x) ) of ( f(x) = \frac{{2x - 1}}{{x - 1}} ) is ( f^{-1}(x) = \frac{{x + 1}}{{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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- What is the difference between #y=(x+3)^2# and #y=x^2+3#?
- How do you identify all asymptotes or holes and intercepts for #f(x)=((2+x)(2-3x))/(2x+3)^2#?
- How do you find the inverse of #f(x) = 12/sqrtx#?

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