Question

Graph y=sin^-1(-1/2x) on interval -5≤x≤5.

Answer 1

The answer is C I just took the test.

Answer 2

C

Explanation:

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

So, when

`-2\le x\le 2,`

we have that

`-1\le -(1)/(2)x\le 1.`

This gives us the domain
`-2\le x\le 2` of the function
`y=\sin^(-1)\left(-(1)/(2)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)/(2)x\right)` is the same (options B and D are false).

When x=-2,

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

So, option A is false and option C is true.