SOLUTION: The one-to-one function f is defined below. =f(x)=x/5x-4 Find f^-1, where f^-1 is the inverse of f . Also state the domain and range of f^-1 in interval notation.

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Question 1110100: The one-to-one function f is defined below.
=f(x)=x/5x-4
Find f^-1, where f^-1 is the inverse of f
.
Also state the domain and range of f^-1 in interval notation.

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The domain of f(x) is all values except 4/5.

That means the range of f^-1(x) is all values except 4/5.

To find f^-1(x), switch x and y in the given function and solve for the new y.










The domain of f^-1(x) is all values except 1/5.

Graphing the function and the inverse confirm these results.

The graph of f(x) (red) has a vertical asymptote at x=4/5 and a horizontal asymptote at y=1/5 (green).



The graph of f^-1(x) (red) has a vertical asymptote at x=1/5 and a horizontal asymptote at y = 4/5 (green).



ANSWER:
f^-1(x) = 4x/(5x-1)
Domain: x not = 1/5
Range: y not = 4/5

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