What is the inverse of the functionf(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.