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 ), 0 ≤ x ≤ 1, 0 ≤ x 1, 0 x 1, 0 x ≤ 1

MARKS App · 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

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