Question

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

• A. $40\%$
• B. $50\%$
• C. $30\%$
• D. $65\%$

Answer 1

Answer: (A)

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