Question

I don't understand....
Given the functions f(x)= x+2 and g(x) = x^2, what values of x result in f(g(x))=g(f(x))?

Answer 1

Have you considered creating the two functions and solving the resultant equation?

Answer 2

^

Answer 3

f(g(x)) = f o g
g(f(x)) = g o f
so

f(g(x)) = x^2 + 2
g(f(x)) = (x+2)^2

now just set these two equal to each other and solve..
x^2 + 2 = (x+2)^2