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Question

If f(x)={x1, x1,2x22, x<1g(x)={x+1, x>0x2+1, x0 and h(x)=|x|,then limx 0f(g(h(x))) is

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Solution

limx 0+f(g(h(x)))=f(g(0+))=f(1+)=0
limx 0f(g(h(x)))=f(g(0+))=f(1+)=0
Hence, limx 0f(g(h(x)))=0

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