STD 12 - 1. relation and function — JEE कक्षा 11 साइन्स — Question

Let ${f_1} = \frac{1}{{4 - {x^2}}}$   and   ${f_2} = {\log _{10}}\left( {{x^3} - x} \right)$

$ \Rightarrow 4 - {x^2} \ne 0\,\,\,\,\,\,\,\,\,\,\,\,\,{x^3} - x > 0$

$ \Rightarrow x \ne  \pm 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow x\left( {x + 1} \right)\left( {x + 1} \right) > 0$

$x \in \left( { - 1,0} \right) \cup \left( {1,\infty } \right) - \left\{ 2 \right\}$

$x \in \left( { - 1,0} \right) \cup \left( {1,2} \right) \cup \left( {2,\infty } \right)$