Answer
The answers are
$(f+g)(x)=-7x+5$
$(f−g)(x)=-x-5$
$(fg)(x)=12x^2−20x$
$(\frac{f}{g})(x)=\frac{-4x}{-3x+5}$.
Work Step by Step
Given functions are
$f(x)=-4x$ and $g(x)=−3x+5$
$(f+g)(x)=f(x)+g(x)$
Substitute values.
$(f+g)(x)=-4x−3x+5$
$(f+g)(x)=-7x+5$
$(f−g)(x)=f(x)−g(x)$
Substitute values.
$(f−g)(x)=-4x−(−3x+5)$
$(f−g)(x)=-4x+3x-5$
$(f−g)(x)=-x-5$
$(fg)(x)=f(x) \times g(x)$
Substitute values.
$(fg)(x)=(-4x)×(−3x+5)$
$(fg)(x)=12x^2−20x$
$(\frac{f}{g})(x)=\frac{f(x)}{g(x)}$
Substitute values.
$(\frac{f}{g})(x)=\frac{-4x}{-3x+5}$.
