Question

What is the inverse of the function f(x) = 2x - 3

A. f ^ - 1 * (x) = - 2x + 3

B. f ^ - 1 * (x) = 1/(2x - 3)

C. f ^ - 1 * (x) = (x + 3)/2

D. f ^ - 1 * (x) does not exist

Answer 1

To find the inverse of the function \( f(x) = 2x - 3 \), we follow these steps:

1. Replace \( f(x) \) with \( y \):
\[
y = 2x - 3
\]

2. Swap \( x \) and \( y \):
\[
x = 2y - 3
\]

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

Now, we replace \( y \) with \( f^{-1}(x) \):
\[
f^{-1}(x) = \frac{x + 3}{2}
\]

Thus, the correct answer is:
C. \( f^{-1}(x) = \frac{x + 3}{2} \)