To find the inverse of a function, first, let's switch f(x) with y
[tex] y=5x + 12 [/tex]
Now, change all the x's into y's and change all the y's into x's
[tex]x=5y+12[/tex]
Now, let's solve this equation in terms of y.
Subtract both sides by 12
[tex] x-12 = 5y [/tex]
Divide both sides by 5
[tex] \frac{x}{5} - \frac{12}{5} =y[/tex]
Flip the equation so we have the y on the left
[tex]y=\frac{x}{5} - \frac{12}{5}[/tex]
Now, replace the y with [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x)=\frac{x}{5} - \frac{12}{5}[/tex]
That's your answer. If you need any clarifications, feel free to comment.
Have an awesome day! :)
