To find the inverse, we switch the "x" and "y" variables in the equation and solve for the "new y". The new "y" is actually the inverse function, or y^(-1) or f^(-1)(x). Note: f(x) is the same as y, its just different notation. And y^(-1) is the same as f^(-1)(x).
y=2x-1 becomes x=2y-1.
Solving for the "new y", which we change it to y^(-1):
x=2y^(-1)-1
x+1=2y^(-1)
(x+1)/2=y^(-1).
And that's it! Your inverse function, f^(-1)(x)= (x+1)/2.
