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 ))

Question

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 )) (A) 0 ≤ x ≤ 1 (B) 0 ≤ x< 1 (C) 0< x< 1 (D) 0< x ≤ 1

Tardigrade Admin · Accepted Answer

f(x)+g(x)=√x+√1-x, domain [0,1] f(x)-g(x)=√x-√1-x, domain [0,1] g ( x )-f( x )=√1- x -√ x , domain [0,1] (f( x )/ g ( x ))=(√ x /√1- x ), domain [0,1) ( g ( x )/f( x ))=(√1- x /√ x ), domain (0,1] So, common domain is (0,1)

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

$0 \leq x \leq 1$

$0 \leq x < 1$

$0 < x < 1$

$0 < x \leq 1$

$f (x) + g (x) = x + 1 - x$ , domain $[0, 1]$
$f (x) - g (x) = x - 1 - x$ , domain $[0, 1]$
$g (x) - f (x) = 1 - x - x$ , domain $[0, 1]$
$\frac{f ( x )}{g ( x )} = \frac{x}{1 - x}$ , domain $[0, 1)$
$\frac{g ( x )}{f ( x )} = \frac{1 - x}{x}$ , domain $(0, 1]$
So, common domain is $(0, 1)$

Q. 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)=g(x)f(x)​

0≤x≤1

0≤x<1

0<x<1

0<x≤1