Chapter 4.7, Problem 27PPS

To determine

To find: The inverse of the function $3y-x=3$ .

Answer to Problem 27PPS

The inverse of the function $3y-x=3$ is $f^{-1}\left(x\right)=3x-3$ .

Explanation of Solution

Given:

The function is $3y-x=3$ .

Concept used:

To obtain the inverse of any function $f\left(x\right)=ax+b$ , following steps are used:

Replace $f\left(x\right)$ with $y$ .

Interchange $x$ and $y$ .

Solve for $y$ .

Again, replace $y$ with $f\left(x\right)$ .

Calculation:

Interchange $x$ and $y$ in the given expression $3y-x=3$ .

  $3x-y=3$

Solve for $y$ in expression $3x-y=3$ as follows:

  $\begin{array}{c}3x-y=3\\ -y=3-3x\\ y=3x-3\end{array}$

Replace $y$ with $f^{-1}\left(x\right)$ in above equation to obtain the inverse of the function.

  $f^{-1}\left(x\right)=3x-3$

Thus, the inverse of the function $3y-x=3$ is $f^{-1}\left(x\right)=3x-3$ .