If \( f(x)=x+|x|+\cos \left(\left[\pi^{2}\right] x\right) \) and \(...

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If \( f(x)=x+|x|+\cos \left(\left[\pi^{2}\right] x\right) \) and \( g(x)=\sin x \), where [.] denotes the greatest integer function, then
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(1) \( f(x)+g(x) \) is continuous everywhere
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(2) \( f(x)+g(x) \) is differentiable everywhere
(3) \( f(x) \times g(x) \) is differentiable everywhere
(4) \( f(x) \times g(x) \) is continuous but not differentiable at \( x=0 \)
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