Question

If f(x) =5x + 12 what is f-1(x)

Answer 1

To find the inverse of a function, first, let's switch f(x) with y

$y=5x + 12$

Now, change all the x's into y's and change all the y's into x's

$x=5y+12$

Now, let's solve this equation in terms of y.

Subtract both sides by 12

$x-12 = 5y$

Divide both sides by 5

$\frac{x}{5} - \frac{12}{5} =y$

Flip the equation so we have the y on the left

$y=\frac{x}{5} - \frac{12}{5}$

Now, replace the y with $f^{-1}(x)$

$f^{-1}(x)=\frac{x}{5} - \frac{12}{5}$

That's your answer. If you need any clarifications, feel free to comment.

Have an awesome day! :)