Answer:
The inverse of f(x) = 4x is h(x) = (1/4)x, or h(x) = x/4
Step-by-Step Procedure:
Let's go through the actual steps to determine the correct inverse, h(x), of the given function f(x) = 4x.
1. Start by replacing the label "f(x)" with y: y = 4x
2. Interchange the variables x and y: x = 4y
3. Solve this equation for y: y = x/4
4. Replace the label "y" with h(x): h(x) = x/4. Note that this h(x) is the inverse of the function f(x). Also note that "x/4" is clearer and less ambiguous than 1/4x (which could mistakenly be read as "1 over 4x").
Match this up with the fourth possible answer: h(x) = (1/4)x