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

MCQ

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

A
$( - 3,\; - 2.5) \cup ( - 2.5,\; - 2)$
✓
$( - 2,\;0) \cup (0,\;1)$
C
$(0, 1)$
D
None of these

✓

Answer

Correct option: B.

$( - 2,\;0) \cup (0,\;1)$

b
(b) $x + 2 \ge 0$ $i.e.,$ $x \ge - 2{\rm{ or }} - 2 \le x$

$\because {\log _{10}}(1 - x) \ne 0$==> $1 - x \ne 1$==> $x \ne 0$

Again $1 - x > 0$ ==> $1 > x$ ==> $x < 1$

All these can be combined as $ - 2 \le x < 0$ and $0 < x < 1$.

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