If $f (x) = x + 2$ and $g (x) = x^2$, then for what value of $x$ does $f(g(x)) = g(f(x))$? Express your answer as a common fraction.
-1/2
f(g(x)) = x^2 + 2
g(f(x) ) = (x + 2)^2
So.....we want to know
x^2 + 2 = (x + 2)^2 simplify
x^2 + 2 = x^2 + 4x + 4 subtract x^2 from both sides
2 = 4x + 4 subtract from both sides
-2 = 4x divide both sides by 4
-2 / 4 = x = - 1 /2