Chapter 4.7, Problem 51PFA

To determine

The inverse function of a given equation.

Answer to Problem 51PFA

The inverse function is $f^{-1}(x)=-\frac{3}{2}x+4\frac{1}{2}$ .

Explanation of Solution

Given information:

An equation given $2x+3y=9$ .

Calculation:

The given equation is $2x+3y=9$ .

To find inverse function first we swap x and y in the equation.

By swapping x and y, we will get,

  $\begin{array}{l}2y+3x=9\\ \Rightarrow 2y=9-3x\\ \Rightarrow y=\frac{1}{2}(9-3x)\\ \Rightarrow y=\frac{9}{2}-\frac{3}{2}x\\ \Rightarrow y=-\frac{3}{2}x+\frac{9}{2}\\ \Rightarrow y=-\frac{3}{2}x+4\frac{1}{2}\end{array}$

By using the notation $f^{-1}(x)$ , we can write,

  $f^{-1}(x)=-\frac{3}{2}x+4\frac{1}{2}$

Option D is correct.