The domain of the definition of the function f(x) = (3 /4-x2) + log10 (x3 -x) is :

Question

The domain of the definition of the function f(x) = (3 /4-x2) + log10 (x3 -x) is : (A) ( 1 , 2 ) ∪ (2, ∞) (B) ( - 1 , 0 ) ∪ (1, 2) ∪ (3, ∞)  (C) ( - 1 , 0 ) ∪ (1, 2) ∪ (2, ∞)  (D) ( - 2 , -1 ) ∪ ( -1, 0) ∪ (2, ∞)

Tardigrade Admin · Accepted Answer

4 - x2 ≠ 0 ; x3 - x > 0 ∴ Df ∈ (-1 , 0) ∪ (1,2) ∪ (2, ∞)

Q. The domain of the definition of the function $f (x) = \frac{3}{4 - x ^{2}} + lo g_{10} (x^{3} - x)$ is :

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

$(- 1, 0) \cup (1, 2) \cup (3, \infty)$

$(- 1, 0) \cup (1, 2) \cup (2, \infty)$

$(- 2, - 1) \cup (- 1, 0) \cup (2, \infty)$

$4 - x^{2} \neq = 0; x^{3} - x > 0$
$∴ D_{f} \in (- 1, 0) \cup (1, 2) \cup (2, \infty)$

Q. The domain of the definition of the function f(x)=4−x23​+log10​(x3−x) is :

(1,2)∪(2,∞)

(−1,0)∪(1,2)∪(3,∞)

(−1,0)∪(1,2)∪(2,∞)

(−2,−1)∪(−1,0)∪(2,∞)