What is the inverse of the function f(x) = 2x + 1?

First, conceptually understand what an inverse function is, it makes solving it very intuitive.  An inverse function is simply a function which has points (y,x) for every point (x,y) of the parent function.  So you are essentially taking all points of the parent function and switching the x and y coordinates for each.  Those switched coordinates are produced by the "inverse function".

Mathematically then, finding the inverse function is a matter of solving for x and then switching the variable labels.  In this case:

y=2x+1  subtract 1 from both sides

y-1=2x  divide both sides by 2

(y-1)/2=x  now just switch the labels for the variables...

y=(x-1)/2  so

f^-1(x)=(x-1)/2  is the inverse of f(x)=2x+1