1. ## quotient values

given that g: real number ->real number and for all x which are quotient numbers, g(x) =o. show that g is 0 function.

what i did was i tried to divide the real line into small intervals of quotient values.
and tried to say that by intermediate value thm, all values have to be 0..but i dont think that works right?

2. It's false without any additional assumptions. I'm guessing that g is supposed to be continuous in this exercise. The general fact is that two continuous functions which agree on a dense subset are the same function (at least when the codomain is a reasonable space, which R certainly is).

Here's a hint for showing it in this particular case: suppose g(x) is nonzero for some x. Then...hmm...I don't think I can say anything further without giving it all away. Use continuity.