Suppose you plan to paint the outside of your house.
Let $g$ be the function that determines the number of gallons of paint needed in terms of the number of square feet of walls needed to be painted. Let $h$ be the function that determines the cost (in dollars) in terms of $m$ gallons of paint.
Which of the following expressions represents the cost (in dollars) to paint 500 square feet of wall?
$g(h(500))$
$g^{-1}(500)$
$h(g(500))$
$g(500)$
$h(500)$

Step 1 ：Suppose you plan to paint the outside of your house.

Step 2 ：Let \(g\) be the function that determines the number of gallons of paint needed in terms of the number of square feet of walls needed to be painted.

Step 3 ：Let \(h\) be the function that determines the cost (in dollars) in terms of \(m\) gallons of paint.

Step 4 ：The question is asking for the cost to paint 500 square feet of wall.

Step 5 ：We first need to find out how many gallons of paint are needed for 500 square feet using the function \(g\), and then find out the cost for that amount of paint using the function \(h\).

Step 6 ：This corresponds to the expression \(h(g(500))\).

Step 7 ：\(\boxed{h(g(500))}\) is the correct expression that represents the cost (in dollars) to paint 500 square feet of wall.