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

Question

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

Smart Achievers · Accepted Answer

(2)

$x + 2 \geq 0 \Rightarrow x \geq - 2$

$∵$ $\log_{10} (1 - x) \neq 0 \Rightarrow 1 - x \neq 1 \Rightarrow x \neq 0$

Again, $1 - x > 0 \Rightarrow x < 1$

All these can be combined as $- 2 \leq x < 0 or 0 < x < 1$

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