Question
The domain of definition of $$f\left( x \right) = \frac{{{{\log }_2}\left( {x + 3} \right)}}{{{x^2} + 3x + 2}}$$ is
A.
$$\frac{R}{{\left\{ { - 1, - 2} \right\}}}$$
B.
$$\left( { - 2,\infty } \right)$$
C.
$$\frac{R}{{\left\{ { - 1, - 2, - 3} \right\}}}$$
D.
$$\frac{{\left( { - 3,\infty } \right)}}{{\left\{ { - 1, - 2} \right\}}}$$
Answer :
$$\frac{{\left( { - 3,\infty } \right)}}{{\left\{ { - 1, - 2} \right\}}}$$
Solution :
$$\eqalign{
& {\text{For}}\,{\text{domain}}\,{\text{of}}\,f\left( x \right) = \frac{{{{\log }_2}\left( {x + 3} \right)}}{{{x^2} + 3x + 2}} \cr
& {x^2} + 3x + 2 \ne 0\,{\text{and}}\,x + 3 > 0 \cr
& \Rightarrow x \ne - 1, - 2\,{\text{and}}\,x > - 3 \cr
& \therefore {D_f} = \left( { - 3,\infty } \right) - \left\{ { - 1, - 2} \right\} \cr} $$