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: Recall inverse - tangent definition

The inverse - tangent function, $y = \tan^{-1}(x)$, is defined as the angle $y$ (in radians) such that $\tan(y)=x$ and $y\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$.

Step2: Substitute $x = 0$

We need to find $y$ such that $\tan(y)=0$ and $y\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$. We know that $\tan(0)=0$.

Answer:

A. $0$