alleryFor 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.
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