Question

f(x) = x² – 2x + 3; [0, 3] → A. Find whether f(x) is injective or not. Also find the set A, if f(x) is surjective.

Answer 1

f′(x) = 2(x – 1); 0 ≤ x ≤ 3

∴ f(x) is not monotonic. Hence it is not injective. 

For f(x) to be surjective, A should be equal to its range. By graph range is [2, 6] 

∴ A ≡ [2, 6]