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  4. The domain of the function f(x)= log 10 (x-5/x2-10 x+24)-3 √x+5 is

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Q. The domain of the function $f(x)=\log _{10} \frac{x-5}{x^2-10 x+24}-3 \sqrt{x+5}$ is

Relations and Functions

Solution:

$\frac{x-5}{x^2-10 x+24}>0 \text { and } x+5>0 $
$\Rightarrow x >5, x >6 \Rightarrow x >6 \Rightarrow x \in(6, \infty) $
$\text { or } x< 5, x >4 \Rightarrow 4< x< 5 \Rightarrow x \in(4,5)$