Question

Graph y=sin^-1 (1/4 x) on the interval -5≤x≤5.

Answer 1

Answer:

D

Step-by-step explanation:

The arcsine ($\sin^{-1}$) function of x is defined as the inverse sine function of x when -1≤x≤1.

So, when

$-4\le x\le 4,$

we have that

$-1\le \dfrac{1}{4}x\le 1.$

This gives us the domain $-4\le x\le 4$ of the function $y=\sin^{-1}\left(\dfrac{1}{4}x\right).$

The range of the function $y=\sin^{-1}x$ is $-\dfrac{\pi }{2}\le x\le \dfrac{\pi }{2},$ so the range of the function $y=\sin^{-1}\left(\dfrac{1}{4}x\right)$ is the same (options A and C are false).

When x=-4,

$y=\sin^{-1}\left(\dfrac{1}{4}\cdot (-4)\right)=\sin^{-1}(-1)=-\dfrac{\pi}{2}.$

So, option B is false and option D is true.