Question

Which function below is the inverse of f(x)=2x+3 over 5?

Answer 1

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