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