What is the inverse of the function f(x) = 4x + 8?

To find the inverse of the function f(x) = 4x + 8, we start by replacing f(x) with y:

y = 4x + 8

Next, we swap x and y. This gives us:

x = 4y + 8

Now, we need to solve for y:

1. Subtract 8 from both sides:
2. x – 8 = 4y
3. Next, divide both sides by 4:
4. y = (x – 8)/4

Therefore, the inverse function is:

f^-1(x) = (x – 8)/4

In summary, we found the inverse of the function by first swapping the variables and then solving for y. This process allows us to express the output in terms of the input of the inverse function.