1. ## Graphing 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?

2. ## Re: Graphing Trig Functions

Originally Posted by Manni
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?
Since the tangent and arctangent functions are inverse functions, this is just 2x...

3. ## Re: Graphing Trig Functions

Originally Posted by Prove It
Since the tangent and arctangent functions are inverse functions, this is just 2x...
not quite. what if $x = \frac{\pi}{4}$...?

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

see for yourself: y &#61; arctan&#40;tan&#40;2x&#41;&#41; - Wolfram|Alpha

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