Question

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

Explanation:

Step1: Set $y = f(x)$

$y = 2x + 1$

Step2: Swap $x$ and $y$

$x = 2y + 1$

Step3: Solve for $y$

Subtract 1 from both sides: $x - 1 = 2y$
Divide by 2: $y = \frac{1}{2}x - \frac{1}{2}$

Answer:

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