Question

Assertion :A function $y=f\left(x\right)$ defined by $x^2-{\cot }^{-1}y=\pi$ then domain of $f\left(x\right)$ is $R$ Reason: ${\cot }^{-1}y\in (0,\pi )$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

Given $x^2-{\cot }^{-1}y=\pi$

$\Rightarrow x^2-\pi ={\cot }^{-1}y$
Now, since ${\cot }^{-1}y\in (0,\pi )$

$\Rightarrow 0<x^2-\pi <\pi$

$\Rightarrow \pi <x^2<2\pi$

$x\in (-\sqrt{2\pi },-\sqrt{\pi })\cup (\sqrt{\pi },\sqrt{2\pi })$

$\Rightarrow$ Assertion $\left(A\right)$ is false but Reason $\left(R\right)$ is true.