# Thread: 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 $\displaystyle f(x) = (x-1)^2$ , $\displaystyle x > 1$ ; $\displaystyle f^{-1}(x) = 1 + \sqrt{x}$ , $\displaystyle x > 0$

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

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

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# inverse of piecewise functions

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