If , then…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

If f(x)={x−3,x<0x2−3x+2,x≥0f(x)=\begin{cases}x-3,&x<0\\x^2-3x+2,&x\geq0\end{cases}, then g(x)=f(∣x∣)g(x)=f(|x|) is (1) g′(0+)=−3g'(0^+)=-3 (2) g′(0−)=−3g'(0^-)=-3 (3) g′(0+)=g′(0−)g'(0^+)=g'(0^-) (4) g(x)g(x) is not continuous at x=0x=0

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