1. Tardigrade
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  4. If the functions are defined as f(x)=√x and g ( x )=√1- x , then what is the common domain of the following functions: f+ g , f- g , f / g , g / f, g-f where (f ± g )( x )= f( x ) ± g ( x ),(f / g )( x )=(f( x )/ g ( x ))

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Q. 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 $(f \pm g )( x )=$ $f( x ) \pm g ( x ),(f / g )( x )=\frac{f( x )}{ g ( x )}$

JEE MainJEE Main 2021Relations and Functions

Solution:

$f(x)+g(x)=\sqrt{x}+\sqrt{1-x}$, domain $[0,1]$
$f(x)-g(x)=\sqrt{x}-\sqrt{1-x}$, domain $[0,1]$
$g ( x )-f( x )=\sqrt{1- x }-\sqrt{ x }$, 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 $(0,1)$