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?

Question

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?, g ( f ( S ) ) ≠ S, f ( g ( S ) ) ≠ f ( S ), f g S = S, g f S = g S

MARKS App · Accepted Answer

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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