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
Match the Columns
Match the conditions/expressions in Column I with statement in Column II.
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Answer:
Correct Answer: 9. (d)
Solution:
- For domain of $y$,
$$ \begin{array}{cccl} & 1-x>0,1-x \neq 1 \quad \text { and } & x+2>0 \\ \Rightarrow & x<1, x \neq 0 \text { and } & x>-2 \\ \Rightarrow & -2<x<1 \text { excluding } 0 & \\ \Rightarrow & & x \in(-2,1)-{0} \end{array} $$
