What is the range of `f(x)=x^(3)-sqrt(-x-6)` ?

Options

A. All real numbers less than or equal to - 222
B. All real numbers than or equal to - 216
C. All real numbers greater than or equal to - 216
D. All real numbers greater than or equal to 216

Answer

B

Explanation

The expression under the eadical must have a value greater than or equal to 0. Therefore,
`-x - 6 ge 0`
`- x ge 6`
`x le -6`
`f(-6)=(-6)^(3)-sqrt(-(-6)-6)=-216`
For any x less than or equal to `-6, f(x), le -216`.