Question

3) Find the equation representing the inverse of the givenfunction. Check answer using your responses to previousproblems. (Type or insert picture of your work and final answer.)y = f(x) = 3x - 5

Answer 1

$f^{-1}(x)=\frac{x}{3}+\frac{5}{3}\text{ }$

1) To find the inverse function of a linear one, we must follow some steps:

2) Take the given function, and swap the variables so

$y=3x-5$

It's going to become in the process:

$x=3y-5$

3) And rewrite it putting y on the left side:

$\begin{gathered} -3y=-x-5 \\ 3y=x+5 \\ \frac{3y}{3}=\frac{x}{3}+\frac{5}{3} \\ y=\frac{x}{3}+\frac{5}{3}\text{ or} \\ f^{-1}(x)=\frac{x}{3}+\frac{5}{3}\text{ } \end{gathered}$

So that's our inverse function whose Range is the Domain of the original one and the Domain is the Range of the original one.