Answer
$a. 2$
$b. 22$
$c. x^2+2$
$d. x^2+10x+22$
$e. 5$
$f. -2$
$g. x+10$
$h. x^4-6x^2+6$
Work Step by Step
$f(x)=x+5$
$g(x)=x^2-3$
$a.\quad f(g(0))=?$
$f(g(x))=(x^2-3)+5=x^2+2$
$f(g(0))=0^2+2=2$
$b.\quad g(f(0))=?$
$g(f(x))=(x+5)^2-3=x^2+10x+25-3$
$g(f(0))=22$
$c.\quad f(g(x))=x^2+2$
$d.\quad g(f(x))=x^2+10x+22$
$e.\quad f(f(-5))=?$
$f(f(x))=(x+5)+5=x+10$
$f(f(-5))=-5+10=5$
$f.\quad g(g(2))=?$
$g(g(x))=(x^2-3)^2-3=x^4-6x^2+9-3$
$=x^4-6x^2+6$
$g(g(2))=2^4-6(2)^2+6=16-24+6$
$=-2$
$g.\quad f(f(x))=x+10$
$h.\quad g(g(x))=x^4-6x^2+6$
