Let f(x)=√ cos -1 √1-x2- sin -1 x Statement-1: Range of f ( x ) is [0, √π] Statement-2: The value of the function increases as x increases in its domain.

Question

Let f(x)=√ cos -1 √1-x2- sin -1 x Statement-1: Range of f ( x ) is [0, √π] Statement-2: The value of the function increases as x increases in its domain. (A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1. (B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. (C) Statement-1 is true, statement-2 is false. (D) Statement-1 is false, statement-2 is true

Tardigrade Admin · Accepted Answer

For x ≥ 0 f ( x )=0 and for x <0, f(x)=√-2 sin -1 x ⇒ range of f ( x ) is [0, √π] ∴ Statement- 1 is true but Statement- 2 is false

Q. Let $f (x) = cos^{- 1} 1 - x^{2} - sin^{- 1} x$
Statement-1 : Range of $f (x)$ is $[0, π]$
Statement-2 : The value of the function increases as $x$ increases in its domain.

Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

Statement-1 is true, statement-2 is false.

Statement-1 is false, statement-2 is true

For $x \geq 0 f (x) = 0$ and for $x < 0$ ,
$f (x) = - 2 sin^{- 1} x$
$\Rightarrow$ range of $f (x)$ is $[0, π]$
$∴$ Statement- 1 is true but Statement- 2 is false

Q. Let f(x)=cos−11−x2​−sin−1x​ Statement-1 : Range of f(x) is [0,π​] Statement-2 : The value of the function increases as x increases in its domain.