Question

which represents the inverse of the function f(x) = 4x?
○ h(x) = x + 4
○ h(x) = x − 4
○ h(x) = \frac{3}{4}x
○ h(x) = \frac{1}{4}x

Explanation:

Step1: Recall inverse function steps

To find the inverse of a function \( f(x) \), we first replace \( f(x) \) with \( y \), so \( y = 4x \). Then we swap \( x \) and \( y \), getting \( x = 4y \).

Step2: Solve for \( y \)

To solve \( x = 4y \) for \( y \), we divide both sides by 4: \( y=\frac{1}{4}x \). So the inverse function \( h(x)=\frac{1}{4}x \).

Answer:

\( h(x)=\frac{1}{4}x \) (the fourth option)