Question

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

Explanation:

Step1: Replace \( f(x) \) with \( y \)

We start with the function \( f(x) = 2x + 1 \). Replace \( f(x) \) with \( y \), so we have \( y = 2x + 1 \).

Step2: Swap \( x \) and \( y \)

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

Step3: Solve for \( y \)

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

Answer:

\( h(x)=\frac{1}{2}x-\frac{1}{2} \) (the first option: \( h(x)=\frac{1}{2}x-\frac{1}{2} \))