Chapter 1.2, Problem 1QR

To determine

To find: The value of $f^{-1}(x)$

Answer to Problem 1QR

The value of $f^{-1}(x)=\frac{x+3}{2}$

Explanation of Solution

Given information: The fraction is $f(x)=2x-3$

Calculation:

The given fraction is:

  $f(x)=2x-3$

The first step in determining the inverse function is to switch x and y.

  $y=2x-3$

  $x=2y-3$

To both sides, add 3.

  $x+3=2y$

Divide all sides by 2, then perform the inverse.

  $\frac{x+3}{2}=y$

  $f^{-1}(x)=\frac{x+3}{2}$

Here $f(x),y=x$ , and $f^{-1}(x)$ (to enlarge the image of the graph to clearly see the units on the axes)

  

Therefore the required value of $f^{-1}(x)=\frac{x+3}{2}$