FunctionHard
Question
Which of the following pair of functions are identical -
Options
A.f(x) = sin-1 x + cos-1 x and g(x) = 
B.f(x) = tan-1 x + cot-1 x and g(x) =
C.f(x) = sec-1 x + cosec-1 x and g(x) =
D.All of these
Solution
(A) f(x) = sin-1x + cos-1x, x ∈ [-1, 1] and g(x) = 
, x ∈ R
f(x) =
, x ∈ [-1, 1] and g(x) = 
, x ∈ R Non-identical functions
(B) f(x) = tan-1x + cot-1x and g(x) =
, x ∈ R
f(x) =
, x ∈ R and g(x) = 
x ∈ R Identical functions
(C) f(x) = sec-1x + cosec-1x and g(x) =
, x ∈ R
f(x) =
′ |x| ∈ [1, ∞) and g(x) = 
, x ∈ R Non-identical functions
, x ∈ Rf(x) =
, x ∈ [-1, 1] and g(x) = , x ∈ R Non-identical functions(B) f(x) = tan-1x + cot-1x and g(x) =
, x ∈ Rf(x) =
, x ∈ R and g(x) = x ∈ R Identical functions(C) f(x) = sec-1x + cosec-1x and g(x) =
, x ∈ Rf(x) =
′ |x| ∈ [1, ∞) and g(x) = , x ∈ R Non-identical functionsCreate a free account to view solution
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