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JEE Main201910 Apr 2019Morning ShiftMathematicsFunctionsActual

Let f x = x 2 , x ∈ R . For any A ⊆ R , define g A = x ∈ R : f ( x ) ∈ A . If S = [ 0 , 4 ] , then which one of the following statements is not true?

Options

  1. Ag ( f ( S ) ) ≠ S
  2. Bf ( g ( S ) ) ≠ f ( S )
  3. Cf g S = S
  4. Dg f S = g S

Correct answer

D. g f S = g S

Step-by-step solution

From the given information we can conclude g S = - 2,2 , So, f ( g ( S ) ) = 0 , 4 = S And f ( S ) = 0 , 16 ⇒ f g S ≠ f S Also, g f S = - 4 , 4 ≠ g S So, g f S ≠ S Hence, g f S = g S is not true.

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