Answer
$(g-h)(x)=3x^3-6x^2-x-5$.
$(g-h)(-1)=-13$.
Work Step by Step
The given functions are
$g(x)=x^3-x^2-5x-4$
$h(x)=-2x^3+5x^2-4x+1$
$(g-h)(x)=g(x)-h(x)$
Plug the given functions
$(g-h)(x)=(x^3-x^2-5x-4)-(-2x^3+5x^2-4x+1)$
Clear the parentheses.
$(g-h)(x)=x^3-x^2-5x-4+2x^3-5x^2+4x-1$
Add like terms.
$(g-h)(x)=3x^3-6x^2-x-5$
Plug $x=-1$
$(g-h)(-1)=3(-1)^3-6(-1)^2-(-1)-5$
Clear the parentheses.
$(g-h)(-1)=-3-6+1-5$
Simplify.
$(g-h)(-1)=-13$.
