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Question

Which of the following functions are identical?

A
f(x)=ln x2 and g(x)=2 ln x
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B
f(x)=logxe and g(x)=1logex
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C
f(x)=sin (cos1x) and g(x)=cos (sin1x)
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D
None of these
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Solution

The correct options are
B f(x)=logxe and g(x)=1logex
C f(x)=sin (cos1x) and g(x)=cos (sin1x)
For the two functions to be identical, their range and domain should be same.f(x) = ln x2 & g(x) = 2 ln x the domain of f is R (0}, while the domain of g is R+so, f and g are not identicalf(x)=logxe & g(x) = 1logex,the domain of f and g is R+ (1}and f(x)=logxe = 1logex = g(x)so, f and g are identicalf(x) = sin (cos1x) & g(x) = cos (sin1x),the domain of f and g are [1, 1]and f(x) = sin (cos1x) =sin (π2sin1x) (sin1x + cos1x = π2, for x [1, 1] )=cos(sin1x)=g(x)so, f and g are identical

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