Domain of the function f(x)= log 3+x(x2-1) is

Question

Domain of the function f(x)= log 3+x(x2-1) is (A)  (-3,-1)∪ (1,∞ )  (B)  (-3,-1)∪ [1,∞ )  (C)  (-3,-2)∪ (-2,-1)∪ (1,∞ )  (D)  [-3,-2)∪ (-2,-1)∪ [1,∞ )

Tardigrade Admin · Accepted Answer

f(x) is defined when x2-1>0, ⇒ x2>1 ⇒ x<-1 and x>1 Also, 3+x>0 and x≠ -2 ∴ x>-3 and x≠ -2 ∴ Domain =(-3,-2)∪ (-2,-1)∪ (1,∞ )

Q. Domain of the function $f (x) = lo g_{3 + x} (x^{2} - 1)$ is

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

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

$(- 3, - 2) \cup (- 2, - 1) \cup (1, \infty)$

$[- 3, - 2) \cup (- 2, - 1) \cup [1, \infty)$

$f (x)$ is defined when $x^{2} - 1 > 0,$
$\Rightarrow$ $x^{2} > 1$
$\Rightarrow$ $x < - 1$ and $x > 1$
Also, $3 + x > 0$ and $x \neq = - 2$
$∴$ $x > - 3$ and $x \neq = - 2$
$∴$ Domain $= (- 3, - 2) \cup (- 2, - 1) \cup (1, \infty)$

Q. Domain of the function f(x)=log3+x​(x2−1) is

(−3,−1)∪(1,∞)

(−3,−1)∪[1,∞)

(−3,−2)∪(−2,−1)∪(1,∞)

[−3,−2)∪(−2,−1)∪[1,∞)