FunctionHard
Question
Which of the following pair of functions are identical ?
Options
A.
, sin 
+ cos 
, sin + cos B.sin-1 
, 2 tan-1 x
, 2 tan-1 xC.
D. ln x3 + ln x2, 5 ln x
Solution
(A) 
sin
+ cos 
non-identical function
(B) sin-1
= 2 tan-1 x, x ∈ [-1, 1] only
2 tan-1 x, x ∈ R non-identical function
(C) √x2 = |x|, x ∈ R
(√x)2 = x, x ∈ R+ U {0} non-identical function
(D) lnx3 + ln x2 = 5 lnx, x > 0
5lx , x > 0 identical function
sin
+ cos non-identical function(B) sin-1
= 2 tan-1 x, x ∈ [-1, 1] only 2 tan-1 x, x ∈ R non-identical function
(C) √x2 = |x|, x ∈ R
(√x)2 = x, x ∈ R+ U {0} non-identical function
(D) lnx3 + ln x2 = 5 lnx, x > 0
5lx , x > 0 identical function
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