Domain of definition of the function f(x) = [3 4 - x^2] + [ _10( x^3 - x )], is

Question

Domain of definition of the function f(x) = $${3 \over {4 - {x^2}}}$$ + $${\log _{10}}\left( {{x^3} - x} \right)$$, is

Accepted Answer

$$f\left( x \right) = {3 \over {4 - {x^2}}} + {\log _{10}}\left( {{x^3} - x} \right)$$

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

$$x \ne  \pm \sqrt 4 $$ and $- 1 < x < 0$

or $$\,\,\,1 < x < \infty $$

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

$$D = \left( { - 1,0} \right) \cup \left( {1,2} \right) \cup \left( {2,\infty } \right).$$

Solutions · 1