Question

Let f(x) = x², 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?
(A) f(g(S) ≠ f(S) (B) f(g(S)) = S
(C) g(f(S)) ≠ S (D) g(f(S)) = g(S)

Answer 1

Answer:

Let f(x) = x², 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?

(A) f(g(S) ≠ f(S)

(B) f(g(S)) = S

(C) g(f(S)) ≠ S

(D) g(f(S)) = g(S)✔✔

Answer 2

Answer:

Let f(x) = x², 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?

(A) f(g(S) ≠ f(S)

(B) f(g(S)) = S

(C) g(f(S)) ≠ S

(D) g(f(S)) = g(S)✔