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

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

Sagot :

GinnyAnswer
To find the inverse of the function \( f(x) = 4x \), we will follow these steps:

1. Express the function in terms of \( y \) instead of \( f(x) \):
[tex]\[ y = 4x \][/tex]

2. Swap \( x \) and \( y \) to find the inverse:
[tex]\[ x = 4y \][/tex]

3. Solve for \( y \) to express the inverse function in terms of \( x \):
[tex]\[ y = \frac{x}{4} \][/tex]

Thus, the inverse function can be written as:
[tex]\[ h(x) = \frac{x}{4} \][/tex]

4. Among the given choices, the one that matches our derived inverse function is:
[tex]\[ h(x) = \frac{1}{4}x \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
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