The function f(x)= cot -1 √(x+3) x+ cos -1 √x2+3 x+1 is defined on the set S, where S=

Question

The function f(x)= cot -1 √(x+3) x+ cos -1 √x2+3 x+1 is defined on the set S, where S= (A)  0,3  (B) (0,3) (C)  0,-3  (D) [-3,0]

Tardigrade Admin · Accepted Answer

x ( x +3) ≥ 0 ⇒ x ≥ 0 text or x ≤-3 text and -1 ≤ x2+3 x+1 ≤ 1 ⇒ x(x+3) ≤ 0 text Hence -3 ≤ x ≤ 0 text Hence x =0 text or -3 ⇒ x = 0,-3

Q. The function $f (x) = cot^{- 1} (x + 3) x + cos^{- 1} x^{2} + 3 x + 1$ is defined on the set $S$ , where $S =$