32Composing f(g(2)), g(f(2))

$\displaystyle f(x) = 3x - 2$ and $\displaystyle g(x) = x^2 + 1$. Find $\displaystyle f(g(2))$ and $\displaystyle g(f(2))$.

f(g(2)) = 13 and g(f(2)) = 17. Composing means plugging the inner answer into the outer function: g(2) = 5, then f(5) = 3(5) − 2 = 13; and f(2) = 4, then g(4) = 4² + 1 = 17. Order matters, since the two results differ.