I got a question from a friend, who is tutoring high school students for Math after school. The question is basically this:
Does writing $f(x) = x^2$ mathematically mean the same as $F(x) = x^2$?
I read from other S.E sections that function notations are conventions, not fixed rules. How will my friend explain to her students about when to (mathematically correct) use notations $f(x)$, $g(x)$, $h(x)$ or $F(x)$, $G(x)$, $H(x)$?