The domain of the function f (x)=( log2(x+3)/x2+3x+2) is

Question

The domain of the function f (x)=( log2(x+3)/x2+3x+2) is (A) R - -1,-2  (B) R - -1,-2 ,0  (C) (-3 ,-1) ∪ (-1, ∞) (D) (-3, ∞) - -1,-2

Tardigrade Admin · Accepted Answer

Given function is f(x)=( log 2(x+3)/x2+3 x+2) Here, for existence of log x+3> 0 ⇒ x > -3 ⇒ x ∈(-3, ∞) and for existence of f(x), x2+3 x+ 2 ≠ 0 ⇒ (x+1)(x+2) ≠ 0 ⇒ x ≠-1,-2 Hence, required domain of f(x) is (-3, ∞)- -1,-2

Q. The domain of the function $f (x) = \frac{l o g _{2} ( x + 3 )}{x ^{2} + 3 x + 2}$ is

$R - {- 1, - 2}$

$R - {- 1, - 2, 0}$

$(- 3, - 1)$ $\cup$ $(- 1, \infty)$

$(- 3, \infty) - {- 1, - 2}$

$(0, \infty)$

Q. The domain of the function f(x)=x2+3x+2log2​(x+3)​ is

R−{−1,−2}

R−{−1,−2,0}

(−3,−1) ∪ (−1,∞)

(−3,∞)−{−1,−2}

(0,∞)