Inverse Tan Function

1. The problem statement, all variables and given/known data

State the range

y=inverse tan( 2x)
3. The attempt at a solution

The original range of inverse tan is ( -pi/2, pi/2)

Should tan inverse (2x) have (-pi, pi) as its range?
 

HallsofIvy

Science Advisor
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No. 2x changes x values, the domain, not the range. The range of tan-1(x) is (-pi/2, pi/2) because as x goes to negative infinity, tan-1[/sup](x) goes to -pi/2 and as x goes to infinity, tan-1(x) goes to pi/2.

As x goes to -infinity, what does 2x go to? What does tan-1
(2x) go to?
As x goes to infinity, what does 2x go to? What does tan-1
(2x) go to?
 

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