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  4. The number of integers in the domain of the function f(x)=√ log (1/2)|x-2|+2 is

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Q. The number of integers in the domain of the function $f(x)=\sqrt{\log _{\frac{1}{2}}|x-2|+2}$ is

Relations and Functions - Part 2

Solution:

$\log _{\frac{1}{2}}|x-2| \geq-2 \Rightarrow|x-2| \leq 4 \Rightarrow-4 \leq x-2 \leq 4$
$-2 \leq x \leq 6 \Rightarrow \text { Number of integers }=8(x \neq 2) $