Question

what is the inverse of the function $f(x) = 2x + 1$?
$\circ\\ h(x) = \frac{1}{2}x - \frac{1}{2}$
$\circ\\ h(x) = \frac{1}{2}x + \frac{1}{2}$
$\circ\\ h(x) = \frac{1}{2}x - 2$
$\circ\\ h(x) = \frac{1}{2}x + 2$

Explanation:

Step1: Replace f(x) with y

We start by writing the function as \( y = 2x + 1 \).

Step2: Swap x and y

To find the inverse, we swap the roles of x and y, so we get \( x = 2y + 1 \).

Step3: Solve for y

First, subtract 1 from both sides: \( x - 1 = 2y \). Then, divide both sides by 2: \( y=\frac{1}{2}x-\frac{1}{2} \). So the inverse function \( h(x)=\frac{1}{2}x - \frac{1}{2} \).

Answer:

A. \( h(x)=\frac{1}{2}x-\frac{1}{2} \)