Question

I NEED HELP LOLLL
What is the value of g(-4)?

Answer 1

Option B: 1

Explanation:

Given the piecewise-defined function rules:

`\displaystyle\mathsf{\left g(x)=\Bigg\{{{\sqrt[3]{x+5},\quad\ x\leq -4} \atop {-x^2+11,\quad\ x\:>-4}} \right. }`

The piecewise-defined function defines the rules over specific intervals of its domain.

In order to find the value of g( –4), we must first determine which piecewise-defined function applies to an input value of x = –4. This input value does not fall under the second piecewise-defined function since the input , x > –4 Thus, x = -4 is not included as part of the solution.

The piecewise-defined function that applies to g( –4) is
`\displaystyle\mathsf{g(x)=\:\sqrt[3]{x+5}}` because of the rule, "x ≤ –4."

All we need to do at this point is to substitute the input value into the following piecewise-defined function:

`\displaystyle\mathsf{g(x)=\:\sqrt[3]{x+5}}`

`\displaystyle\mathsf{g(-4)=\:\sqrt[3]{-4+5}}`

`\displaystyle\mathsf{g(-4)=\:\sqrt[3]{1}}`

`\displaystyle\mathsf{g(-4)=\:1}`

Therefore, the value of g( –4) = 1, which makes Option B the correct answer.