91Ó°ÊÓ

Let \([x]\) denotes the integral part of \(x \in R \cdot g(x)=x-[x]\). Let \(f(x)\) be any continuous function with \(f(0)=f(1)\), then the function \(h(x)=f(g(x))\) (a) has finitely many discontinuities (b) is discontinuous at some \(x=c\) (c) is continuous on \(R\) (d) is a constant function.

The function \(f(x)=\sqrt{1-\sqrt{1-x^{2}}}\) (a) has its domain \(-1 \leq x \leq 1\) (b) has finite one sided derivates at the point \(x=0\) (c) is continuous and differentiable at \(x=0\) (d) is continuous but not differentiable at \(x=0\)