Question

select the correct answer.
what is the value of \\( g(-4) \\)?
\\( g(x) = \

$$\begin{cases} \\sqrt3{x + 5}, & x \\leq -4 \\\\ -x^2 + 11, & x > -4 \\end{cases}$$

\\( \text{a. } -5 \\)\\( \text{b. } 27 \\)\\( \text{c. } -1 \\)\\( \text{d. } 1 \\)

Explanation:

Step1: Choose correct piece of function

Since $x=-4$ satisfies $x \leq -4$, use $g(x)=\sqrt[3]{x+5}$.

Step2: Substitute $x=-4$ into formula

$$g(-4)=\sqrt[3]{-4+5}$$

Step3: Simplify the expression

$$g(-4)=\sqrt[3]{1}=1$$

Answer:

D. 1