Let $f\left(x\right)=\{\left[x\right]x\in Ix-1x\in I$ (where [.] denotes the greatest integer function) and $g\left(x\right)=\{\sin x+\cos x,x<01,x\ge 0$ . Then for $f\left(g\left(x\right)\right)atx=0$${\left(\lim \right)}_{x\vec{0}}f\left(g\left(x\right)\right)$ exists but not continuous Continuous but not differentiable at $x=0$ Differentiable at $x=0$${\left(\lim \right)}_{x\vec{0}}f\left(g\left(x\right)\right)$ does not exist $f\left(x\right)$ is continuous but not differentiable

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