The question give us a function equation 2f(x) - f(1/x) = 3x, and ask for f(x). Let 2f(x) - f(1/x) = 3x as equation1. Change x to 1/x and 1/x to x. We get
2f(1/x) - f(x) = 3/x as equation2. We need to remove f(1/x), multiply 2 to equation1. We get 4f(x) - 2f(1/x) = 6x, name it as equation3. Add equation2 and equation3, ~~2f(1/x)~~ - f(x) + 4f(x) - ~~2f(1/x)~~ = 3/x + 6x. Simplify it, 3f(x) = 3/x + 6x = (3 + 6x^{2})/x = 3(1 + 2x^{2})/x.
Both sides of the equation divide by 3, we get f(x) = (2x^{2} + 1)/x