Answer
$a.\quad 10$
$b.\quad -4$
$c.\quad 16$
$d.\quad 18$
Work Step by Step
$\left[\begin{array}{lll}
x & f(x) & \\
x=0 & f(0)=(-0)^{3}-(0)^{2}-(0)+10 & \\
& =10 & \\
& & \\
x=2, & f(2)=(-2)^{3}-(2)^{2}-(2)+10 & \\
& =-8-4-2+10 & \\
& =-4 & \\
& & \\
x=-2 & f(-2)=(-(-2))^{3}-(-2)^{2}-(-2)+10 & \\
& =(2)^{3}-4+2+10 & \\
& =8-4+2+10 & \\
& =16 & \\
& & \\
x=1 & f(1)=(-1)^{3}-(1)^{2}-(1)+10 & \\
& =-1-1-1+10 & \\
& =7 & \\
x=-1 & f(-1)=(-(-1))^{3}-(-1)^{2}-(-1)+10 & \\
& =1^{3}-1+1+10 & \\
& =11 &
\end{array}\right.$
$f(1)+f(-1)=7+11=18$