What is the inverse of the function y = 3x + 9?

Finding the Inverse of the Function

To find the inverse of the given function y = 3x + 9, we will follow a step-by-step process. The inverse function essentially swaps the roles of x and y.

Step 1: Replace y with x

Start by rewriting the equation as:

x = 3y + 9

Step 2: Solve for y

Next, we need to isolate y. To do this, subtract 9 from both sides:

x - 9 = 3y

Then, divide both sides by 3:

y = (x - 9) / 3

Step 3: Write the Inverse Function

The equation we found for y is the inverse function. We can denote the inverse function as f^-1(x):

f-1(x) = (x - 9) / 3

Conclusion

Therefore, the inverse of the function y = 3x + 9 is:

f-1(x) = (x - 9) / 3