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 (cosâˆ’1x) and g(x)=cos (sinâˆ’1x)For the two functions to be identical, their range and domain should be same.â†’f(x) = ln x2 & g(x) = 2 ln x the domain of f is R âˆ’ (0}, while the domain of g is R+so, f and g are not identicalâ†’f(x)=logxe & g(x) = 1logex,the domain of f and g is R+ âˆ’ (1}and f(x)=logxe = 1logex = g(x)so, f and g are identicalâ†’f(x) = sin (cosâˆ’1x) & g(x) = cos (sinâˆ’1x),the domain of f and g are [âˆ’1, 1]and f(x) = sin (cosâˆ’1x) =sin (Ï€2âˆ’sinâˆ’1x) (sinâˆ’1x + cosâˆ’1x = Ï€2, for x âˆˆ[âˆ’1, 1] )=cos(sinâˆ’1x)=g(x)so, f and g are identical

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