If f(x) = x + 9 and h(x) = 5x - 3, find a function g such that g of f = h.

To find the function g such that g of f equals h, we need to substitute f(x) into g and set it equal to h(x). Here's how you can find g:

Step 1: Write down the expression for g(x), replacing x with f(x).
g(f(x)) = h(x)

Step 2: Replace f(x) with its definition x + 9 in g(f(x)).
g(x + 9) = h(x)

Step 3: Simplify the expression g(x + 9) on the left side of the equation.
g(x) + 9 = h(x)

Step 4: Replace h(x) with its expression 5x - 3.
g(x) + 9 = 5x - 3

Step 5: Solve the equation for g(x).
Subtract 9 from both sides:
g(x) = 5x - 3 - 9
g(x) = 5x - 12

So, the function g such that g(f) = h is g(x) = 5x - 12.