Question

What percent of domain of the function $f\left(x\right)=\sqrt{9-x^2}.\log (9-[2x+5])$ consists of all positive numbers.
Where $[.]$ denotes greatest integer function

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

Answer 1

The correct option is A $40\%$

$9-x^2\ge 0\Rightarrow x\in [-3,3]$
& $9-[2x+5]>0\Rightarrow [2x+5]<9$
$\Rightarrow [2x+5]\le 8\Rightarrow 2x+5<9\Rightarrow x<2$
Hence domain of $f\left(x\right)$ is $x\in [-3,2)$
$\%$ of domain that is positive is $\frac{2}{5}\times 100=40\%$