Question

Find the range of $f\left(x\right)=x^3-\sqrt{-x-6}$

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

Answer 1

The correct option is B All real numbers less than or equal to $-216$

$f\left(x\right)=x^3-\sqrt{-x-6}$

Find the domain of a square root function.

Find the domain and range of a function from the algebraic form.

Functions are a correspondence between two sets, called the domain and the range. When defining a function, you usually state what kind of numbers the domain $\left(x\right)$ and range $\left(f\right(x\left)\right)$ values can be.

Then $x\le -6$

Then range $(-6{)}^3\le -216$

So, range all real numbers less then or equal to $-216$.