To find the inverse of the function [tex]\( f(x) = 4x \)[/tex], we need to follow these steps:
### Step 1: Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]
Start by setting [tex]\( y = 4x \)[/tex].
### Step 2: Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]
To find the inverse function, interchange [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[
x = 4y
\][/tex]
### Step 3: Solve for [tex]\( y \)[/tex]
Next, solve this equation for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{x}{4}
\][/tex]
This [tex]\( y \)[/tex] is the expression for the inverse function. Therefore, the inverse function is given by:
[tex]\[
h(x) = \frac{1}{4}x
\][/tex]
### Conclusion
Among the provided options:
- [tex]\( h(x) = x + 4 \)[/tex]
- [tex]\( h(x) = x - 4 \)[/tex]
- [tex]\( h(x) = \frac{3}{4}x \)[/tex]
- [tex]\( h(x) = \frac{1}{4}x \)[/tex]
The correct choice representing the inverse of the function [tex]\( f(x) = 4x \)[/tex] is:
[tex]\[
h(x) = \frac{1}{4}x
\][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{h(x) = \frac{1}{4} x} \][/tex]
