To determine the inverse of the function [tex]\( f(x) = 4x \)[/tex], we can follow these detailed steps:
1. Start with the original function:
[tex]\[ f(x) = 4x \][/tex]
2. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[ y = 4x \][/tex]
3. Solve for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
[tex]\[ x = \frac{y}{4} \][/tex]
4. Replace [tex]\( y \)[/tex] with [tex]\( x \)[/tex] to denote the inverse function [tex]\( h(x) \)[/tex]:
[tex]\[ h(x) = \frac{x}{4} \][/tex]
Therefore, the inverse of the function [tex]\( f(x) = 4x \)[/tex] is given by:
[tex]\[ h(x) = \frac{1}{4} x \][/tex]
Thus, the correct representation of the inverse function is:
[tex]\[ h(x) = \frac{1}{4} x \][/tex]
So, the answer is:
[tex]\[ \boxed{h(x) = \frac{1}{4} x} \][/tex]
