Question

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

• A. Domain of $f(x)+g(x)$ is $\{1\}$
• B. Domain of $g(x)+h(x)$ is $[\sqrt{2}, \infty)$
• C. Domain of $h ( x )+ f ( x )$ is $\left[\frac{1}{\sqrt{2}}, 1\right]$
• D. Domain of $f ( x )+ g ( x )+ h ( x )$ is $\phi$

Answer 1

Answer: (A), (B), (D)

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