evaluate the function $f(x)=\tan^{-1}(x)$ when $x = 0$. give your answer in radians.\n0\n$pi$\n$\frac{3pi}{2}…

evaluate the function $f(x)=\tan^{-1}(x)$ when $x = 0$. give your answer in radians.\n0\n$pi$\n$\frac{3pi}{2}$\n$2pi$

evaluate the function $f(x)=\tan^{-1}(x)$ when $x = 0$. give your answer in radians.\n0\n$pi$\n$\frac{3pi}{2}$\n$2pi$

Answer

Explanation:

Step1: Substitute x value

Substitute (x = 0) into (y=\tan^{- 1}(x)), so (y=\tan^{-1}(0)).

Step2: Recall inverse - tangent property

We know that (\tan(0)=0), and the range of (y = \tan^{-1}(x)) is ((-\frac{\pi}{2},\frac{\pi}{2})). If (\tan(y)=x), then (\tan^{-1}(x)=y). When (x = 0), (y = 0) since (\tan(0)=0) and (0\in(-\frac{\pi}{2},\frac{\pi}{2})).

Answer:

A. 0