Let f(x) = √x+2 and g(x) = x^2 - 2, then find f ○ g and g ○ f

Question

Would appreciate a step by step for this problem so I truly understand it.

Answer 1

f(x) = sqrx + 2

g(x) = x^2 -2

fog = f(g(x)) = f(x^2-2) = sqr(x^2-2)+2

replace x by g(x), i.e. replace x by x^2-2

gof = g(f(x) = g(sqrx + 2) = (sqrx+2)^2 -2

= x + 4sqrx + 4-2

= x +4sqrx + 2

replace x by f(x), i.e. replace x by sqrx +2