Question

The domain of the function $\sqrt{(x^2+2x+3)}+\sqrt{(1-x)}$ is

• A. $(-\infty ,1]$
• B. $R$
• C. $R-\left\{1\right\}$
• D. $[1,\infty )$

Answer 1

The correct option is A $(-\infty ,1]$

For $f\left(x\right)$ to be defined,
$x^2+2x+3\ge 0$
$\Rightarrow (x+1{)}^2+2\ge 0$
$\Rightarrow x\in R\cdots \left(1\right)$
and $1-x\ge 0$
$\Rightarrow x\le 1\cdots \left(2\right)$
From $\left(1\right)$ and $\left(2\right),$ we get
Domain as $(-\infty ,1]$