Answer :
Given:
There are given the function:
[tex]f(x)=(-x)^3-x^2-x+15[/tex]Explanation:
From the given operation:
[tex]f(2)+f(-2)[/tex]Then,
First, we need to find the value of f(2):
Then,
To find the value of f(2), we need to put 2 for x into the given function:
[tex]\begin{gathered} f(x)=(-x)^{3}-x^{2}-x+15 \\ f(x)=(-2)^3-2^2-2+15 \\ f(x)=-8-4-2+15 \\ f(x)=-14+15 \\ f(x)=1 \end{gathered}[/tex]And,
We need to find the value for f(-2).
So,
Put -2 for x into the given function:
Then,
[tex]\begin{gathered} f(x)=(-x)^{3}-x^{2}-x+15 \\ f(-2)=(-(-2))^3-(-2)^2-(-2)+15 \\ f(-2)=8-4+2+15 \\ f(-2)=21 \end{gathered}[/tex]Then,
[tex]\begin{gathered} f(2)+f(-2)=1+21 \\ =22 \end{gathered}[/tex]Final answer:
Hence, the correct option is 22.