graph the inverse circular function.\n$y = \\tan^{-1}(x)$
graph the inverse circular function.\n$y = \\tan^{-1}(x)$
Answer
Explanation:
Step1: Analyze the domain and range
The domain of (y = \tan^{-1}(x)) is ((-\infty,\infty)) and the range is ((-\frac{\pi}{2},\frac{\pi}{2})). The function (y=\tan^{-1}(x)) is an increasing function.
Step2: Check the behavior as (x\to\pm\infty)
As (x\to\infty), (y = \tan^{-1}(x)\to\frac{\pi}{2}) (horizontal asymptote (y=\frac{\pi}{2})). As (x\to-\infty), (y=\tan^{-1}(x)\to-\frac{\pi}{2}) (horizontal asymptote (y =-\frac{\pi}{2})). Also, when (x = 0), (y=\tan^{-1}(0)=0).
Answer:
A.