Is arctan(tan(2x)) an example of a composite function? In other words, would the range of tan2x become the domain of arctanx? Also, is the domain for this composite function the union between the domains of tan2x and arctanx?

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- Oct 16th 2011, 08:47 PMManniGraphing Trig Functions
Is arctan(tan(2x)) an example of a composite function? In other words, would the range of tan2x become the domain of arctanx? Also, is the domain for this composite function the union between the domains of tan2x and arctanx?

- Oct 16th 2011, 10:32 PMProve ItRe: Graphing Trig Functions
- Oct 17th 2011, 12:15 AMDevenoRe: Graphing Trig Functions
not quite. what if $\displaystyle x = \frac{\pi}{4}$...?

also, the range of arctan is (-1,1). but we can easily imagine an original input of, oh say 2.

see for yourself: y = arctan(tan(2x)) - Wolfram|Alpha

the function is not defined for all real x, and is not even equal to 2x except on (-pi/4,pi/4).