Question

Find the domain of $f\left(x\right)=\sqrt{x+2}+lo{g}_{10}(1-x)$

Answer 1

$f\left(x\right)=\sqrt{x+2}+lo{g}_{10}(1-x)$

Domain of $\sqrt{x+2}$

$x+2>0$

$x>-2...\left(1\right)$

Domain of $lo{g}_{10}(1-x)$

$1-x>0$

$x<1...\left(2\right)$

From the conditions (1) and (2), we

can say that the Domain of $f\left(x\right)$ is

$xϵ(-2,1)$