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  4. What percent of the domain of the function f(x)=(√9-x2/√[4]9-|2 x+5|) consists of positive numbers.

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Q. What percent of the domain of the function $f(x)=\frac{\sqrt{9-x^2}}{\sqrt[4]{9-|2 x+5|}}$ consists of positive numbers.

Relations and Functions - Part 2

Solution:

$ 9-x^2 \geq 0 \Rightarrow -3 \leq x \leq 3$
$\text { also } 9-|2 x+5|>0 $
$\text { i.e. } |2 x+5|<9$
$ -9< 2 x+5< 9 $
$ -7< x< 2$
Hence domain of $f(x)$ is $[-3,2)$
$\%=\frac{2}{5}=40 \%$