## You're correct! Apologies for the confusion. In this case, if we want to find the inverse function y(x) of y = (2x + 1) / (x + 3), we can follow a different approach without the need for a second interchange of x and y.

To find the inverse function, we start with the original equation:

y = (2x + 1) / (x + 3)

Step 1: Swap x and y:

x = (2y + 1) / (y + 3)

Step 2: Solve for y:

Multiply both sides of the equation by (y + 3) to eliminate the denominator:

x(y + 3) = 2y + 1

Expand and rearrange terms:

xy + 3x = 2y + 1

Step 3: Isolate the y term:

Subtract xy from both sides:

3x = 2y - xy + 1

Rearrange terms:

3x - 1 = y(2 - x)

Step 4: Solve for y:

Divide both sides of the equation by (2 - x):

y = (3x - 1) / (2 - x)

And there you have it! The inverse function of y = (2x + 1) / (x + 3) is y = (3x - 1) / (2 - x).

Remember to always test the inverse function by composing it with the original function. In this case, substituting y = (3x - 1) / (2 - x) into y = (2x + 1) / (x + 3) should result in x.