Functions — Important Questions

[0, ∞)

√x is defined only for x ≥ 0. At x = 0, √0 = 0 is valid. So domain = [0, ∞).

True

By definition, range = f(A) = {f(a): a ∈ A} ⊆ B = co-domain. The range can be a proper subset or equal to the co-domain.

Range of f = Co-domain of f

Onto (surjective) means every element of B has at least one pre-image in A, which is equivalent to Range = Co-domain.

f(x₁) = f(x₂) ⟹ x₁ = x₂

One-one (injective) means distinct inputs give distinct outputs. Equivalently: same output implies same input.