Answer
$a)$ $(f+g)(x)=6x+2$
$b)$ $(f-g)(x)=-4x+6$
$c)$ $(f\cdot g)(x)=5x^{2}+18x-8$
$d)$ $\Big(\dfrac{f}{g}\Big)(x)=\dfrac{x+4}{5x-2}$, where $x\ne\dfrac{2}{5}$
Work Step by Step
$f(x)=x+4;$ $g(x)=5x-2$
For each case, replace $f(x)$ by $x+4$ and $g(x)$ by $5x-2$ and simplify:
$a)$ $(f+g)(x)$
$f(x)+g(x)=(x+4)+(5x-2)=x+4+5x-2=6x+2$
$b)$ $(f-g)(x)$
$f(x)-g(x)=(x+4)-(5x-2)=x+4-5x+2=-4x+6$
$c)$ $(f\cdot g)(x)$
$f(x)\cdot g(x)=(x+4)(5x-2)=5x^{2}-2x+20x-8=...$
$...=5x^{2}+18x-8$
$d)$ $\Big(\dfrac{f}{g}\Big)(x)$
$\dfrac{f(x)}{g(x)}=\dfrac{x+4}{5x-2}$ where $x\ne\dfrac{2}{5}$
