Let f(x)=√( sin -1 x- cos -1 x), g(x)=√( tan -1 x- cot -1 x) and h(x)=√( sec -1 x- operatornamecosec-1 x) then correct statement(s) is (are)

Question

Let f(x)=√( sin -1 x- cos -1 x), g(x)=√( tan -1 x- cot -1 x) and h(x)=√( sec -1 x- operatornamecosec-1 x) then correct statement(s) is (are) (A) Domain of f(x)+g(x) is 1  (B) Domain of g(x)+h(x) is [√2, ∞) (C) Domain of h ( x )+ f ( x ) is [(1/√2), 1] (D) Domain of f ( x )+ g ( x )+ h ( x ) is φ

Tardigrade Admin · Accepted Answer

Correct answer is (a) Domain of f(x)+g(x) is 1 Correct answer is (b) Domain of g(x)+h(x) is [√2, ∞)Correct answer is (d) Domain of f ( x )+ g ( x )+ h ( x ) is φ

Q. Let $f (x) = (sin^{- 1} x - cos^{- 1} x), g (x) = (tan^{- 1} x - cot^{- 1} x)$ and $h (x) = (sec^{- 1} x - cosec^{- 1} x)$ then correct statement(s) is (are)

Domain of $f (x) + g (x)$ is ${1}$

Domain of $g (x) + h (x)$ is $[2, \infty)$

Domain of $h (x) + f (x)$ is $[\frac{1}{2}, 1]$

Domain of $f (x) + g (x) + h (x)$ is $ϕ$

Correct answer is (a) Domain of $f (x) + g (x)$ is ${1}$ Correct answer is (b) Domain of $g (x) + h (x)$ is $[2, \infty)$ Correct answer is (d) Domain of $f (x) + g (x) + h (x)$ is $ϕ$

Q. Let f(x)=(sin−1x−cos−1x)​,g(x)=(tan−1x−cot−1x)​ and h(x)=(sec−1x−cosec−1x)​ then correct statement(s) is (are)

Domain of f(x)+g(x) is {1}

Domain of g(x)+h(x) is [2​,∞)

Domain of h(x)+f(x) is [2​1​,1]

Domain of f(x)+g(x)+h(x) is ϕ