Question

Find the domain of definition of $f\left(x\right)=\frac{{\log }_2(x+3)}{x^2+3x+2}$.

• A. $(-3,\infty )$
• B. $\{-1,-2\}$
• C. $(-3,\infty )-\{-1,-2\}$
• D. $(-\infty ,\infty )$

Answer 1

The correct option is C $(-3,\infty )-\{-1,-2\}$

We know ${\log }_{2}P$

$P>0$

and hence here

$x+3>0\Rightarrow x>-3$

Also,

$x^2+3x+2\ne 0\Rightarrow x^2+x+2x+2\ne 0\Rightarrow x(x+1)+2(x+1)\ne 0\Rightarrow (x+1)(x+2)\ne 0\Rightarrow x\ne -1,-2\therefore x\sum (-3,\infty )-\{-1,-2\}$

Answer C