Let me tell you this first! F(x) is a function, x is an independent variable and x is just a parameter. This parameter can be expressed by any letter or word of X or Y or Z. The equation 2f(x)+f( 1/x)=x you asked is true for any X equation, so the equation 2f (1/x)+f (x) = 1/x is also true. Is there a problem with this equation? Then, for the same x, two f(x) in two formulas must be the same, so are two f( 1/x).

For f(x) and f(x+2), the teacher said that X is different, so it is understood that for f(t), T is an independent variable, which is replaced by X in f(x) and X+2 in f(x+2).