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

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



Answer :

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]