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in Sets, relations and functions by (53.3k points)

Which of the following pair(s) of functions are identical?

(A)  f(x) = cos (2 tan-1x),g(x) = 1 - x2/1 + x2

(B)  f(x) =2x/1 + x,g(x) = sin(2 cot-1x)

(C)   f(x) = tan x + cot x, g(x) = 2 cosec 2x 

(D) f(x) = eIn(sgncot-1 x) , g(x) = eIn[]1+{x}

where sgn(⋅), [⋅], {⋅} denotes signum, greatest integer and fractional part functions, respectively.

1 Answer

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Best answer

Correct option (A, B, C, D)

Domain of f and g both are ‘R’

(B) Domain of f and g both are ‘R’.

(C) Domain of f and g are

(D) Domain of f:

Since, 0 ≤ {x} < 1= 1

Therefore, f(x) and g(x) are identical functions.

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