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Question

If f(x)={|x+1|x0;xx>0; and
g(x)={|x|+2x<2;|x2|x2; then f(x)g(x) is continuous at

A
x=0, x=1
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B
x=1, x=1
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C
x=1, x=0
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D
x=2, x=0
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Solution

The correct option is B x=1, x=1
f(x)=x1x1;x+11<x0;xx>0;
g(x)=x+2x0;x+20<x<2x+2x2;

f(x)=⎪ ⎪⎪ ⎪x1x<1;x+11x0;x0<x<2;xx2;
g(x)=⎪ ⎪⎪ ⎪x+2x1;x+21<x0;x+20<x2;x+2x2;

f(x)g(x)=⎪ ⎪⎪ ⎪3x1;2x11<x0;20<x<2;2x2x2;

Therefore, f(x)g(x) is continuous everywwhere except at x=0, x=2

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