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JEE Main202118 Mar 2021Morning ShiftMathematicsFunctionsActual

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 )

Options

  1. A0 ≤ x ≤ 1
  2. B0 ≤ x < 1
  3. C0 < x < 1
  4. D0 < x ≤ 1

Correct answer

C. 0 < x < 1

Step-by-step solution

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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