Properties of ITF

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Absolute value of sum of all integral values of ‘ $x$ ’ in the domain of $f (x) = \cot^{- 1} (\sqrt{x (x + 3)}) + \cos^{- 1} (\sqrt{x^{2} + 3 x + 1})$ is

Moderate

Solution

$∴ x (x + 3) \geq 0 \Rightarrow x \geq 0$ or $x \leq - 3 ....... (1)$
also $0 \leq x^{2} + 3 x + 1 \leq 1$ $\Rightarrow x^{2} + 3 x \leq 0$
$\Rightarrow x (x + 3) \leq 0 a n d 0 \leq x \leq 3....... (2)$
$\Rightarrow x (x + 3) = 0$
$\Rightarrow$ $x = \{0, - 3\}$
$S u m o f i n t e g r a l v a l u e s o f x = 0 - 3 = - 3$
$∴$ $a b s o l u t e v a l u e o f s u m o f i n t e g r a l v a l u e s o f a = |- 3| = 3$

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Properties of ITF

Remember concepts with our Masterclasses.

Absolute value of sum of all integral values of ‘x’ in the domain of fx=cot−1xx+3+cos−1x2+3x+1is

∴ xx+3≥0⇒x≥0orx≤−3 ....... (1)also 0≤x2+3x+1≤1 ⇒ x2+3x≤0⇒ xx+3≤0 and 0≤x≤3.......(2)⇒ xx+3=0 ⇒ x=0,−3Sum of integral values of x =0-3=-3∴absolute value of sum of integral values of a =-3=3

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Absolute value of sum of all integral values of ‘ $x$ ’ in the domain of $f (x) = \cot^{- 1} (\sqrt{x (x + 3)}) + \cos^{- 1} (\sqrt{x^{2} + 3 x + 1})$ is