QJEEM21Ma8a35: JEE Main 2021 Mathematics - Class 11 JEEM21Ma8a35 Solution: If the functions are defined as and , then what is the common…

Question

Verified Solution • 2025–26 Session moderate

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 where

(f \pm g)(x) = f(x) \pm g(x),(f/g)x = {{f(x)} \over {g(x)}}

Accepted Answer

f + g = \sqrt x + \sqrt {1 - x}

\Rightarrow x \ge 0

&

1 - x \ge 0 \Rightarrow x \in [0,1]

f - g = \sqrt x - \sqrt {1 - x}

\Rightarrow x \ge 0

&

1 - x \ge 0 \Rightarrow x \in [0,1]

f/g = {{\sqrt x } \over {\sqrt {1 - x} }}

\Rightarrow x \ge 0

&

1 - x &gt; 0 \Rightarrow x \in [0,1)

g/f = {{\sqrt {1 - x} } \over {\sqrt x }}

\Rightarrow 1 - x \ge 0

&

x &gt; 0 \Rightarrow x \in (0,1]

g - f = \sqrt {1 - x} - \sqrt x

\Rightarrow 1 - x \ge 0

&

x \ge 0 \Rightarrow x \in [0,1]

\Rightarrow

x \in (0,1)

Step-by-Step Verified Solution