How do you find the inverse of $f (x) = \frac{1}{x - 5}$ $f(x) = \frac{1}{x-5}$ algebraically?

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Answer 1 · 2014-10-24T02:58:36

Step 1:

$f (x) = \frac{1}{x - 5}$ $f(x)=1/(x-5)$

Change $f (x)$ $f(x)$ to $y$ $y$

$y = \frac{1}{x - 5}$ $y=1/(x-5)$

Step 2:

Switch $x$ $x$ and $y$ $y$

$x = \frac{1}{y - 5}$ $x=1/(y-5)$

Step 3:

Solve for $y$ $y$

$x (y - 5) = 1$ $x(y-5)=1$

$\frac{x (y - 5)}{x} = \frac{1}{x}$ $(x(y-5))/x=1/x$

$(y - 5) = \frac{1}{x}$ $(y-5)=1/x$

$y = \frac{1}{x} + 5$ $y=1/x+5$

How do you find the inverse of f(x) = \frac{1}{x-5}f(x)=1x−5f(x) = \frac{1}{x-5} algebraically?