JEE PYQ: Functions Question 4
Question 4 - 2021 (18 Mar Shift 1)
If the functions are defined as $f(x) = \sqrt{x}$ and $g(x) = \sqrt{1 - x}$, then what is the common domain of the following functions: $f + g, f - g, f/g, g/f, g - f$:
(1) $0 \le x \le 1$
(2) $0 \le x < 1$
(3) $(0,1)$
(4) $\emptyset$
Type: MCQ
Show Answer
Answer: (3) $(0,1)$
Solution
$f(x) + g(x) = \sqrt{x} + \sqrt{1 - x}$, domain $[0,1]$
$\frac{f(x)}{g(x)} = \frac{\sqrt{x}}{\sqrt{1-x}}$, domain $[0,1)$
$\frac{g(x)}{f(x)} = \frac{\sqrt{1-x}}{\sqrt{x}}$, domain $(0,1]$
So, common domain is $(0,1)$
BETA
