Inverses are always symmetrical with respect to the line y = x.
A function has an inverse if it passes the horizontal line test. For example, draw y = x^2. This function does NOT have an inverse. However, draw y=x^3 and you will see it does pass the horizontal line test.
To find the inverse of y = 2x, just switch the x-y variables and then solve for y. That is let x = 2y and now solve for y and you will have your inverse. Good Luck