Q.

which pair of functions is identical?

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a

sin−1⁡(sin⁡x) and sin⁡sin−1⁡x

b

loge⁡ex,eloge⁡x

c

loge⁡x2,2loge⁡x

d

None of these

answer is D.

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Detailed Solution

Here, (a) sin−1⁡(sin⁡x) is defined for x∈−π2,π2, while sin⁡sin−1⁡x is defined only for x∈[−1,1] (b) loge⁡ex, is defined for all x, while eloge⁡x is defined for x>0.  (c) loge⁡x2 is defined for all x∈R−{0}, while 2loge⁡x is definedforx>0. Thus, none is identical.
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which pair of functions is identical?