Inverse Function

**scottptrsn** · October 23rd 2008, 06:15 PM

I am having trouble with this problem:

Show that, for every value of a, the function

f(x)= a + (1/(x-a))

is its own inverse.

**vincisonfire** · October 23rd 2008, 06:20 PM

$y= a + \frac{1}{x-a}$
Switch x and y and solve for y to find inverse
$x= a + \frac{1}{y-a}$
$x - a = \frac{1}{y-a}$
$y - a = \frac{1}{x-a}$
$y = a + \frac{1}{x-a}$

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