First of all, u have to know what (f o g)(x) means. It means that the function f is a function of g where g is a function of x. or in other words (f o g)(x)= f(g(x))
as in Q#24:
(f o g)(x)= f(g(x)) but [tex] f(x)=(x+2)^{2}[/tex] so in case of f(g(x)) means that we have to eliminate each x in the function f(x) and substitute it with the value of g(x) as the following:
[tex] f(g(x))=(g(x)+2)^{2}[/tex] but [tex]g(x)=\sqrt{x}-2[/tex] so we have to substitute with the value of g(x) in the last equation
[tex] f(g(x))= (\sqrt{x}-2+2)^{2}=(\sqrt{x})^{2}=x[/tex]
by the same way (g o f)(x), it means that g is a function of f where f is a function of x.
so [tex] (g o f)(x)=g(f(x))=\sqrt{f(x)} -2 =\sqrt{(x+2)^2} -2 =x+2-2 =x [/tex]
If you followed the same procedure, u would figure out how to solve the rest urself.
