Question

8.) What is the inverse function of each of the following? (2 points each) Write your answer in the correct format. a) f(x)=4(3x-5)

Answer 1

Given:

$f(x)=4(3x-5)$

Required:

$f^{-1}(x)$

Solution:

First, set y = 4 ( 3x - 5), then solve for x in terms of y

$\begin{gathered} y=4(3x-5) \\ y=12x-20 \\ y-20=12x \\ 12x=y-20 \\ \frac{12x}{12}=\frac{y-20}{12} \\ x=\frac{y-20}{12} \end{gathered}$

Lastly, write the answer using x as a variable

$f^{-1}(x)=\frac{x-20}{12}$

Answer:

$f^{-1}(x)=\frac{x-20}{12}$