This particular question was asked in quiz yesterday and I was unable to solve it.

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> Suppose f and g are entire functions and g(z) $\neq$0 for all z $\epsilon \mathbb{C} $ . If |f(z) |$\leq$ |g(z) | , the which one of them is true.
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1.f is a constant function.

2.f(0) =0 .

3.for some C $\epsilon \mathbb{C} $ , f(z) = C g(z) .

4.f(z) $\neq$ 0 for all z $\epsilon \mathbb{C} $ .

4 th option can be removed by taking f(z) =0 and g(z) =2 .

But I am unable to find any way to remove rest of options.