# How do you find the inverse of #f(x)=(x+2)/(x-1)# and is it a function?

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To find the inverse of ( f(x) = \frac{x+2}{x-1} ), we first switch the roles of ( x ) and ( y ) and then solve for ( y ).

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

Now, we solve for ( y ):

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

[ xy - x = y + 2 ]

[ xy - y = x + 2 ]

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

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

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

To determine if ( f(x) = \frac{x+2}{x-1} ) is a function, we need to check if for every ( x ) value, there is exactly one corresponding ( y ) value.

Since the function ( f(x) = \frac{x+2}{x-1} ) is defined for all real numbers except ( x = 1 ), it is a function. However, to be more precise, we should also check that the function is not undefined for any values in its domain. In this case, ( f(x) ) is undefined when ( x = 1 ), as it would result in division by zero. Therefore, we need to exclude ( x = 1 ) from the domain of the function. So, ( f(x) = \frac{x+2}{x-1} ) is a function defined for all real numbers except ( 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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