First slide

Functions (XII)

Question

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

Moderate

A

$(- 3, - 2) excluding - 2.5$
B

$[0, 1] excluding 0.5$
C

$[- 2, 1) excluding 0$
D

$none of these$

Solution

The given function is $y = \frac{1}{\log_{10} (1 - x)} - \sqrt{x + 2} is$
For domain
$1 - x > 0 a n d x i s a n o n z e r o r e a l n u m b e r i t i m p l i e s x < 1 a n d x i s n o t e q u a l t o z e r o x + 2 \geq 0 \Rightarrow x \geq - 2 h e n c e, - 2 \leq x < 1 a n d x i s n o t e q u a l t o z e r o T h e r e f o r e, t h e d o m a i n o f t h e g i v e n f u n c t i o n i s [- 2, 1) - \{0\}$

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