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JEE Main202313 Apr 2023Morning ShiftMathematicsFunctionsActual

For x ∈ ℝ , two real valued functions f x and g x are such that, g ( x ) = x + 1 and f o g x = x + 3 - x . Then f 0 is equal to

Options

  1. A1
  2. B5
  3. C0
  4. D- 3

Correct answer

B. 5

Step-by-step solution

We have been given that f g x = x + 3 - x ⇒ f ( x + 1 ) = x + 3 - x Put x + 1 = t x = t - 1 x = ( t - 1 ) 2 ⇒ f ( t ) = ( t - 1 ) 2 + 3 - ( t - 1 ) ⇒ f ( 0 ) = 1 + 3 + 1 = 5 Hence this is the correct option.

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