What is the inverse function of f(x) = 2x + 6?

To find the inverse function of f(x) = 2x + 6, we need to follow a few steps. First, we start by replacing f(x) with y:

y = 2x + 6

Next, we swap the roles of x and y to find the inverse:

x = 2y + 6

Now, we solve for y:

1. Subtract 6 from both sides:

x – 6 = 2y

2. Now, divide both sides by 2:

(x – 6)/2 = y

So, the inverse function is:

f^-1(x) = (x – 6)/2

This inverse function, f^-1(x), effectively undoes the original function f(x). If you apply f^-1 to f(x), you will get back x. This relationship demonstrates how inverse functions work!