Q.

The domain of the function fx=lnx-1x2+4x+4 is

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a

-3,-1∪1,2

b

-2,-1∪2,∞

c

-∞,-3∪-2,-1∪2,∞

d

none of these

answer is C.

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Detailed Solution

Case I01  or   x>2Then    x2+4x+4≥1or   x2+4x+3≥0or    x≥-1   or   x≤-3So,     x∈-∞,-3∪2,∞From  (1)  and  2,x∈-∞,-3∪-2,-1∪2,∞.
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The domain of the function fx=lnx-1x2+4x+4 is