Question

If domain of $f(x)$ is $[-1,4]$, then number of integers in the domain of $g(x)=f(2-\sqrt{x})+f\left(1-x^{\frac{1}{3}}\right)$ is

• A. 6
• B. 7
• C. 8
• D. 9

Answer 1

Answer: (D)

$-1\le 2-\sqrt{x}\le 4\Rightarrow -3\le -\sqrt{x}\le 2\Rightarrow -2\le \sqrt{x}\le 3\Rightarrow 0\le x\le 9$.....(1)
$-1\le 1-x^{\frac{1}{3}}\le 4\Rightarrow -2\le -x^{\frac{1}{3}}\le 3\Rightarrow -3\le x^{\frac{1}{3}}\le 2\Rightarrow -27\le x\le 8$.....(2)
Intersection of (1) \& (2) is $0\le x\le 8$
$\therefore$ Number of integers $=9$