Question

Find the domain of $f\left(x\right)=\frac{3}{4-x^2}+{\log }_{10}(x^3-x)$

• A. $(1,2)$
• B. $(-1,0)\cup (1,2)$
• C. $(1,2)\cup (2,\infty )$
• D. $(-1,0)\cup (1,2)\cup (2,\infty )$

Answer 1

The correct option is D $(-1,0)\cup (1,2)\cup (2,\infty )$

For, f(x) to be defined,

$4-x^2\ne 0$

$\to x\ne \pm 2$

Also, $x^3-x>0$

$\to x(x^2-1)>0$

$\to x\in (-1,0)\cup (1,\infty )$

So, Domain of f(x)

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

Thus, D is the correct answer.