Functions 1 Question 9
9.
The domain of definition of the function
$y=\frac{1}{\log _{10}(1-x)}+\sqrt{x+2}$ is
(1983, 1M)
(a) $(-3,-2)$ excluding -2.5
(b) $[0,1]$ excluding 0.5
(c) $(-2,1)$ excluding 0
(d) None of these
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Answer:
Correct Answer: 9. (c)
Solution:
- For domain of $y$,
$ 1-x>0,1-x \neq 1 \quad \text { and } \quad x+2>0 $
$\Rightarrow x<1, x \neq 0 \quad \text { and } \quad x>-2 $
$\Rightarrow -2<x<1 \text { excluding } 0 $
$\Rightarrow x \in(-2,1)-{0}$
