The domain of the function fx=1/(9-x^2)+log_20x^3-3x is

Correct answer: (D) -√3,0∪√3,3∪3,∞. 9-x^2≠0 and x^3-3x>0 x≠-3,3 ....(1) and xx^2-3>0 ⇒xx+√3x-√3>0 x∈-√3,0∪√3,∞ …. 2 From 1 ∩ 2, we get, x∈-√3,0∪√3,3∪3,∞

Q16 / 87 · NTA Abhyas (JEE Main) 2020 · Mathematics · Functions

The domain of the function $f (x) = \frac{1}{9 - x^{2}} + l o g_{20} (x^{3} - 3 x)$ is

A
$(- \sqrt{3}, 0) \cup (\sqrt{3}, \infty)$
B
$(- \sqrt{3}, 0) \cup (\sqrt{3}, 3)$
C
$(- \sqrt{3}, 0) \cup (3, \infty)$
Correct answer
D
$(- \sqrt{3}, 0) \cup (\sqrt{3}, 3) \cup (3, \infty)$

Solution

$9 - x^{2} \neq 0$ and $x^{3} - 3 x > 0$
$x \neq - 3, 3$ .... $(1)$

and $x (x^{2} - 3) > 0$
$\Rightarrow x (x + \sqrt{3}) (x - \sqrt{3}) > 0$

$x \in (- \sqrt{3}, 0) \cup (\sqrt{3}, \infty)$ …. $(2)$
From $(1)$ $\cap$ $(2)$ , we get,

$x \in (- \sqrt{3}, 0) \cup (\sqrt{3}, 3) \cup (3, \infty)$

Hence, the correct answer is option: 'D'.

The domain of the function fx=19-x2+log20x3-3x is

Solution

More Functions Questions

The domain of the function $f (x) = \frac{1}{9 - x^{2}} + l o g_{20} (x^{3} - 3 x)$ is