Q.
Which of the following functions are identical?
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a
f(x)=lnx2 and g(x)=2lnx
b
f(x)=logxe and g(x)=1logex
c
f(x)=sincos−1x and g(x)=cossin−1x
d
None of these
answer is B.
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Detailed Solution
(1) For f(x)=logx2, x2>0 or x∈R−{0} For g(x)=2logx, x>0 Hence, f(x) and g(x) are not identical.(2) f(x)=logxe=1logex=g(x) Hence, the functions are identical.(3) f(x)=sincos−1x=sinπ2−sin−1x=cossin−1x=g(x) Hence, the functions are identical.
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