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  4. The domain of the function f(x)=(1/ log 10(1-x))+√x+2 is

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Q. The domain of the function $f(x)=\frac{1}{\log _{10}(1-x)}+\sqrt{x+2}$ is

KCETKCET 2022Relations and Functions

Solution:

$1 - x > 0 , 1 - x \neq 1$
$x -1<0 \,\,\,\,\,\,x \neq 0 \,\,\,\,\,\,x +2 \geq 0$
$x <1 \,\,\,\,\,\,x \geq-2$
$\therefore x \in[-2,0) \cup(0,1)$