Question

Find the domain of definition of the following function:
$y=\sqrt{x+1}+\log (1-x).$

Answer 1

$y=\sqrt{x+1}+log(1-x)$

For $y$ to be real and defined,

$x+1$ must be $\ge 0$ $\Rightarrow x\ge -1$

$1-x$ must be $>0\Rightarrow x<1$

Therefore, $x\in (-1,1)$

Domain of $y$ is $x\in [-1,1).$