Question

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

Answer 1

D

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 (1)/(4)x\le 1.`

This gives us the domain
`-4\le x\le 4` of the function
`y=\sin^(-1)\left((1)/(4)x\right).`

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

When x=-4,

`y=\sin^(-1)\left((1)/(4)\cdot (-4)\right)=\sin^(-1)(-1)=-(\pi)/(2).`

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