To find the inverse of the function \( f(x) = 4x \), we will follow these steps:
1. Express the function in terms of \( y \) instead of \( f(x) \):
[tex]\[
y = 4x
\][/tex]
2. Swap \( x \) and \( y \) to find the inverse:
[tex]\[
x = 4y
\][/tex]
3. Solve for \( y \) to express the inverse function in terms of \( x \):
[tex]\[
y = \frac{x}{4}
\][/tex]
Thus, the inverse function can be written as:
[tex]\[
h(x) = \frac{x}{4}
\][/tex]
4. Among the given choices, the one that matches our derived inverse function is:
[tex]\[
h(x) = \frac{1}{4}x
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{4}
\][/tex]
