# Math Help - inverse of a piecewise function

1. ## inverse of a piecewise function

Hi, if I have a piecewise function such as:

f(x) = (x-1)^2 if x>1
or tan(x) if -π/2 < x < 0

If I want want to find the inverse, do I simply calculate the inverse for each of piecewise operations ?
eg. (x-1)^2 has the inverse y = 1 +- sqrt(x)
and tan(x) has the inverse tan^-1(x)

is it is straightforward as that or I am missing something ?
thanks for any help.

2. ## Re: inverse of a piecewise function

Originally Posted by fran1942
Hi, if I have a piecewise function such as:

f(x) = (x-1)^2 if x>1
or tan(x) if -π/2 < x < 0

If I want want to find the inverse, do I simply calculate the inverse for each of piecewise operations ?
eg. (x-1)^2 has the inverse y = 1 +- sqrt(x)
and tan(x) has the inverse tan^-1(x)

is it is straightforward as that or I am missing something ?
the restriction placed on the domain of the original function will be the range of the inverse function ...

for $f(x) = (x-1)^2$ , $x > 1$ ; $f^{-1}(x) = 1 + \sqrt{x}$ , $x > 0$

(note: why is $1 - \sqrt{x}$ not used?)

for $f(x) = \tan{x}$ , $-\frac{\pi}{2} < x < 0$ ; $f^{-1}(x) = \tan^{-1}{x}$ , $x < 0$