Question
The domain of the function $$f\left( x \right) = {\log _{10}}\left( {1 + {x^3}} \right)$$ is :
A.
$$\left( { - 1,\, + \infty } \right)$$
B.
$$\left( {0,\, + \infty } \right)$$
C.
$$\left[ {0,\, + \infty } \right)$$
D.
$$\left( { - 1,\,0} \right)$$
Answer :
$$\left( {0,\, + \infty } \right)$$
Solution :
$$\eqalign{
& {\log _{10}}\left( {1 + {x^3}} \right) > 0 \cr
& {\text{or, }}1 + {x^3} > {10^0} = 1 \cr
& {\text{or, }}{x^3} > 0\,\, \Rightarrow x\, \in \left( {0,\, + \infty } \right) \cr} $$