Answer
$(f+g-h)(x)=-8x^2-2x-1$.
$(f+g-h)(-2)=-29$.
Work Step by Step
The given functions are
$f(x)=-3x^3-2x^2-x+4$
$g(x)=x^3-x^2-5x-4$
$h(x)=-2x^3+5x^2-4x+1$
$(f+g-h)(x)=f(x)+g(x)-h(x)$
Plug the given functions.
$(f+g-h)(x)=(-3x^3-2x^2-x+4)+(x^3-x^2-5x-4)-(-2x^3+5x^2-4x+1)$
Clear the parentheses.
$(f+g-h)(x)=-3x^3-2x^2-x+4+x^3-x^2-5x-4+2x^3-5x^2+4x-1$
Add like terms.
$(f+g-h)(x)=-8x^2-2x-1$
Plug $x=-2$.
$(f+g-h)(-2)=-8(-2)^2-2(-2)-1$
Clear the parentheses.
$(f+g-h)(-2)=-32+4-1$
Simplify.
$(f+g-h)(-2)=-29$.
