Home > Precalculus > Logarithm-- Inverse of an Exponential Function

If f(x) = (x+1) / (x-2), find the inverse of f(x) ?

Answer 1

Madelyn Anderson

Refer to explanation

The domain of f(x) is #R-{2}# and the inverse is

#f(x)=(x-1)/(x+2)=>y=(x-1)/(x+2)=>y*(x+2)=x-1=> y*x+2y=x-1=>2y+1=x-yx=>x=(2y+1)/(1-y)# hence we have that

#f^(-1)(x)=(2x+1)/(1-x)#

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Answer 2

Ariana Alvarez

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

( y = \frac{x+1}{x-2} )

Swap ( x ) and ( y ):

( x = \frac{y+1}{y-2} )

Now, solve this equation for ( y ):

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

( xy - 2x = y + 1 )

( xy - y = 2x + 1 )

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

( y = \frac{2x + 1}{x - 1} )

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

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Answer from HIX Tutor

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.