Question

What is the inverse of the function f(x) = 2x + 1? h(x) = 1/2x - 1/2

h(x) = 1/2x + 1/2
h(x) = 1/2x- 2
h(x) = 1/2x +2 ​

Answer 1

h(x) = x/2 - 1/2

Explanation:

Here's the procedure for finding the inverse function algebraically:

1. Replace the label 'f(x)' with the label 'y:' y = 2x + 1

2. Interchange x and y: x = 2y + 1

3. Solve the resulting equation for y: 2y = x - 1, or y = (1/2)(x - 1) or y = x/2 - 1/2

This result corresponds to the 1st given possible answer choice.

The desired inverse function is h(x) = x/2 - 1/2