Answer
$(g+h-f)(x)=2x^3+6x^2-8x-7$.
$(g+h-f)(-2)=17$.
Work Step by Step
The given functions are
$f(x)=-3x^3-2x^2-x+4$
$g(x)=x^3-x^2-5x-4$
$h(x)=-2x^3+5x^2-4x+1$
$(g+h-f)(x)=g(x)+h(x)-f(x)$
Plug the given functions
$(g+h-f)(x)=(x^3-x^2-5x-4)+(-2x^3+5x^2-4x+1)-(-3x^3-2x^2-x+4)$
Clear the parentheses.
$(g+h-f)(x)=x^3-x^2-5x-4-2x^3+5x^2-4x+1+3x^3+2x^2+x-4$
Add like terms.
$(g+h-f)(x)=2x^3+6x^2-8x-7$
Plug $x=-2$
$(g+h-f)(-2)=2(-2)^3+6(-2)^2-8(-2)-7$
Clear the parentheses.
$(g+h-f)(-2)=-16+24+16-7$
Simplify.
$(g+h-f)(-2)=17$.
