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  4. If domain of f(x)=√((x-1)(7-x)(x-5)4/x(x-5)2) is D, then number of positive integers in D is

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Q. If domain of $f(x)=\sqrt{\frac{(x-1)(7-x)(x-5)^4}{x(x-5)^2}}$ is $D$, then number of positive integers in $D$ is

Relations and Functions - Part 2

Solution:

$\frac{(x-1)(7-x)(x-5)^4}{x(x-5)^2} \geq 0$
$\frac{(x-1)(7-x)}{x} \geq 0, \quad x \neq 5 $
$\Rightarrow x \in(-\infty, 0) \cup[1,7]-\{5\}=D$
$\Rightarrow \text { Number of positive integers in } D=6$