Inverse Tan Function Range: (-pi/2, pi/2)

[missmerisha]

Homework Statement

State the range

y=inverse tan( 2x)

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]

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<sub>-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?}</sub>