Question

What is the inverse of y = 3x -2?

Answer 1

\(\Huge\sf\color{blue}{Welcome\ to\ OpenStudy!}\) @alyssaaldaco

To find the inverse, switch the x and y values, and solve for y.

Answer 2

@DaWizjr Please do not give direct answers.

Answer 3

well, the direct answer given is not correct anyway,.

Answer 4

I will give you an abstract example.

\(\large\color{slate}{\displaystyle \color{blue}{f(x)}=m\color{red}{x}+b}\)

re-writing f(x) as y, for convenience:
\(\large\color{slate}{\displaystyle\color{blue}{y}=m\color{red}{x}+b}\)

switching x and y:
\(\large\color{slate}{\displaystyle \color{red}{x}=m\color{blue}{y}+b}\)

solving for y:
\(\large\color{slate}{\displaystyle \color{red}{x}=m\color{blue}{y}+b}\)

\(\large\color{slate}{\displaystyle \color{red}{x}-b=m\color{blue}{y}}\)

\(\large\color{slate}{\displaystyle \frac{\color{red}{x}-b}{m}=\color{blue}{y}}\) or \(\large\color{slate}{\displaystyle \frac{1}{m}\color{red}{x}-\frac{b}{m}=\color{blue}{y}}\)

this "y" is the inverse function, and proper notation is f^(-1)(x), so:

\(\large\color{slate}{\displaystyle \color{blue}{f^{-1}(x)}=\frac{\color{red}{x}-b}{m}}\) or \(\large\color{slate}{\displaystyle \color{blue}{f^{-1}(x)}=\frac{1}{m}\color{red}{x}-\frac{b}{m}}\)