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

(-2, 1) excluding -1

Solution

For domain of y,
1-x>0. $\Rightarrow x < 1$ and x+2 $\geq$ 0
$\Rightarrow$ x<1, and x $\geq$ -2
$\Rightarrow$ -2 $\leq$ x<1 excluding 0
$x \in [- 2, 1) - \{0\}$

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