Question

Find the inverse of the function. f(x) = 7x + 8

Answer 1

Answer:

$\frac{x-8}{7}$

Step-by-step explanation:

A way to find the inverse function is to swap the x and y (f(x)) in the equation.

$y = 7x + 8\\x = 7y + 8\\x-8 = 7y\\y = \frac{x-8}{7}$

We can check that it is an inverse function by using a property of inverse functions:

$f(g(x)) = x$

If we plug in the f(x) function into the variable x of the inverse function, we should end up with x

$y = \frac{(7x + 8) - 8}{7}\\y = \frac{7x}{7} \\y = x$

It checks out!