What is the inverse of the function

f (x) = 2x+1

Inverses are easy for this problem. First we start with the equation. Then we change the f (x) to y to make this whole problem easier.

y=2x+1

Isolate the x and solve for x.

x = (y-1/2)

Switch x and y again.

y = (x-1/2)

Add function notation.

f^-1 (x) = (x-1/2)

Done! And if you need to check if equations are inverses, add the original equation into the x variable of the inverse. The solution should be f^-1 (x) = x. That means the inverse is right.