First you must grasp what an inverse function really is to make it simple on yourself. If f(x) produces a point (x,y), the inverse function will produce (y,x). That is why it is an "inverse" function because it reverses the x and y coordinates. With that out of the way, mathematically, you simply have to solve the function for the independent variable and then switch the variable labels. Let f(x)=y=(2x+3)/5
y=(2x+3)/5 multiply both sides by 5
5y=2x+3 subtract 3 from both sides
5y-3=2x divide both sides by 2
(5y-3)/2=x now simply reverse the labels for the variables and you have the inverse function of f(x)
y=(5x-3)/2 so
f^-1(x)=(5x-3)/2