Answer
a) $2x$
b) $4$
c) $x^2-4$
d) $\dfrac{x+2}{x-2}$
Domain: $(-\infty,2)\cup(2,\infty)$
Work Step by Step
We are given the functions:
$f(x)=x+2$
$g(x)=x-2$
a) Determine $(f+g)(x)$:
$(f+g)(x)=f(x)+g)(x)=x+2+x-2=2x$
b) Determine $(f-g)(x)$:
$(f-g)(x)=f(x)-g)(x)=x+2-(x-2)=x+2-x+2=4$
c) Determine $(fg)(x)$:
$(fg)(x)=f(x)g)(x)=(x+2)(x-2)=x^2-4$
d) Determine $\left(\dfrac{f}{g}\right)(x)$:
$\left(\dfrac{f}{g}\right)(x)=\dfrac{x+2}{x-2}$
The domain of $\dfrac{f}{g}$ is the set of all real numbers except the zeros of $g$:
$x-2=0\Rightarrow x=2$
The domain is:
$(-\infty,2)\cup(2,\infty)$
