Question

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

h(x) = one-halfx – one-half
h(x) = one-halfx + one-half
h(x) = one-halfx – 2
h(x) = one-halfx + 2

Answer 1

To find the inverse of the function \( f(x) = 2x + 1 \), you need to follow these steps:

1. **Replace \( f(x) \) with \( y \)**:
\[
y = 2x + 1
\]

2. **Swap \( x \) and \( y \)**:
\[
x = 2y + 1
\]

3. **Solve for \( y \)**:
\[
x - 1 = 2y
\]
\[
y = \frac{x - 1}{2}
\]
\[
y = \frac{1}{2}x - \frac{1}{2}
\]

So, the inverse function is:
\[
h(x) = \frac{1}{2}x - \frac{1}{2}
\]

Thus, the correct answer is:
\[
h(x) = \frac{1}{2}x - \frac{1}{2}
\]

Or, in the given options:
\[
h(x) = \text{one-half}x - \text{one-half}
\]