Question

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

Answer 1

Domain of $\sqrt{x+2}+\frac{1}{{\log }_{10}(1-x)}$

$\left(1\right)x+2\ge 0$

$x\ge -2$

$\left(2\right)1-x\ge 0$

$1>x$

$\left(3\right)1-x\ne 1$

$x\ne 0$.

Intersection of all three conditions is $x\in [-2,1]-0$