Which represents the inverse of the function [tex][tex]$f(x)=4x$[/tex][/tex]?

A. [tex][tex]$h(x)=x+4$[/tex][/tex]
B. [tex][tex]$h(x)=x-4$[/tex][/tex]
C. [tex][tex]$h(x)=\frac{3}{4}x$[/tex][/tex]
D. [tex][tex]$h(x)=\frac{1}{4}x$[/tex][/tex]



Answer :

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]