For f: R → R, f(x) = x³, f is:

ANot function

BRandom

CBIJECTION (one-one and onto). f⁻¹(y) = y^(1/3) for all y ∈ R

DMany-one

Answer & Solution

Correct answer: C. BIJECTION (one-one and onto). f⁻¹(y) = y^(1/3) for all y ∈ R

x³: strictly increasing (derivative 3x² ≥ 0). Hence one-one. Range = all R (cube of large x is large; cube of negative is negative). Onto. Bijection. f⁻¹ = cube root.

Practise this question with Quill — GRE →

Keep practising Sets and Relations

Browse all Sets and Relations questions for GRE, or explore more Mathematics topics.

Start a Sets and Relations lesson →