Question

The domain of $\sqrt{x+2}+\frac{1}{{\log }_{10}(x+1)}$ is

• A. $(0,\infty )$
• B. $(-1,\infty )-\left\{0\right\}$
• C. $(-1,0)\cup (1,\infty )$
• D. $R-\{-2,-1\}$

Answer 1

The correct option is B $(-1,\infty )-\left\{0\right\}$

$\sqrt{x+2}+\frac{1}{{\log }_{10}(x+1)}$
For the square root to exist,
$x+2\ge 0$
$\Rightarrow x\ge -2$,
For the $\log$ function, we get
$x+1>0\Rightarrow x>-1$,
For $\frac{1}{{\log }_{10}(x+1)}$ to exist,
${\log }_{10}(x+1)\ne 0\Rightarrow x+1\ne 1\Rightarrow x\ne 0$
$\therefore x\in (-1,\infty )-\left\{0\right\}$