To find the inverse of the function [tex]\( f(x) = 4x \)[/tex], we need to follow a sequence of steps. Here is a detailed, step-by-step solution:
### Step 1: Rewrite the function in terms of [tex]\( y \)[/tex].
Start with the function given:
[tex]\[ f(x) = 4x \][/tex]
Rewrite it as:
[tex]\[ y = 4x \][/tex]
### Step 2: Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
To find the inverse, we swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] in the equation:
[tex]\[ x = 4y \][/tex]
### Step 3: Solve for [tex]\( y \)[/tex].
Solve the equation [tex]\( x = 4y \)[/tex] for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{x}{4} \][/tex]
### Step 4: Rewrite the inverse function.
Replace [tex]\( y \)[/tex] with [tex]\( h(x) \)[/tex] to express the inverse function:
[tex]\[ h(x) = \frac{x}{4} \][/tex]
Alternatively, it can be written as:
[tex]\[ h(x) = \frac{1}{4} x \][/tex]
### Conclusion:
The function representing the inverse of [tex]\( f(x) = 4x \)[/tex] is:
[tex]\[ h(x) = \frac{1}{4} x \][/tex]
So, the correct choice is:
[tex]\[ h(x) = \frac{1}{4} x \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
