Hi Jenna,

Let's try 2 different functions

Let $f(x)=\sqrt{x + 1}$ and $g(x) = 5 - x^2.$ Find $f(g(2)) \mbox{ and }g(f(2)).$

To find $f(g(2))$ you first find $g(2).$

$g(2) = 5 - 2^2 = 1.$

Thus $f(g(2)) = f(1) = \sqrt{1 + 1} = \sqrt{2}.$

To find $g(f(2))$ you need to find $f(2)$ first.

$f(2) = \sqrt{2 + 1} = \sqrt{3}.$

Now $g(f(2)) = g(\sqrt{3}) = 5 - (\sqrt{3})^2 = 5 - 3 = 2.$

Now try your functions.

Penny