To find the inverse of the function [tex]\( f(x) = 4x \)[/tex], we need to follow these steps:
1. Express the function in terms of [tex]\( y \)[/tex]:
[tex]\[
y = 4x
\][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
To find the inverse, we swap the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex], giving us:
[tex]\[
x = 4y
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
To isolate [tex]\( y \)[/tex], we divide both sides of the equation by 4:
[tex]\[
y = \frac{x}{4}
\][/tex]
4. Rewrite the inverse function:
Now, we have [tex]\( y = \frac{x}{4} \)[/tex] which indicates that the inverse function is:
[tex]\[
h(x) = \frac{x}{4}
\][/tex]
This can be rewritten as:
[tex]\[
h(x) = \frac{1}{4} x
\][/tex]
Therefore, the correct choice that represents the inverse of the function [tex]\( f(x) = 4x \)[/tex] is:
[tex]\[
h(x) = \frac{1}{4} x
\][/tex]
