Question

Domain of definition of the function$f\left(x\right)=\frac{3}{4-x^2}+lo{g}_{10}(x^3-x)$

• A. (1, 2)
• B. (-1 , 0)∪(1 , 2)
• C. (1,2)∪(2 ,∞)
• D. (-1 , 0) ∪ (1 , 2)∪( 2, ∞)

Answer 1

The correct option is D (-1 , 0) ∪ (1 , 2)∪( 2, ∞)

$f\left(x\right)=\frac{3}{4-x^2}+lo{g}_{10}(x^3-x).So,4-x^2\ne 0\Rightarrow x\ne \pm \sqrt{4}$

$and{x}^3-x>0\Rightarrow x(x^2-1)>0\Rightarrow -1<x<0andx>1$

$\therefore D=(-1,0)\cup (1,\infty )-\left\{\sqrt{4}\right\}i.e.,D=(-1,0)\cup (1,2)\cup (2,\infty ).$