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Question

Let f(x)=sin1x and g(x)=x2x22x2x6. If g(2)=limx2g(x), then the domain of the function fog is :

A
(,1][2,)
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B
(,2][43,)
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C
(,2][1,)
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D
(,2][32,)
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Solution

The correct option is B (,2][43,)
g(2)=limx2(x2)(x+1)(2x+3)(x2)=37
For domain of f(g(x))
x2x22x2x61
( domain of f(x) is [1,1])
(x+1)2(2x+3)23x2+10x+80
(3x+4)(x+2)0
x ϵ (,2)[43,]

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