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:

  1. 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 $

$\Rightarrow x \in(-2,1)-{0}$



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