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Question

Let f(x)=f1(x)2f2(x),

where, f1(x)={min{x2, |x|}, |x|1 max{x2, |x|}, |x|>1

and, f2(x)={min{x2, |x|}, |x|>1 max{x2, |x|}, |x|1

and, g(x)={min{f(t): 3tx, 3x<0}max{f(t): 0tx, 0x3}

The graph of y=g(x) in its domain is broken at

A
1 point
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B
2 points
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C
3 points
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D
None of these
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Solution

The correct option is A 1 point
f1(x)=x2 and f2(x)=|x|
or, f(x)=f1(x)2f2(x)=x22|x|

Graph of f(x) is

g(x)=⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪f(x), 3x<1 1, 1x<0 0, 0x2 f(x), 2<x3

g(x)=⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪x2+2x, 3x<1 1, 1x<0 0, 0x2 x22x, 2<x3

The graph is broken at x=0

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