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📐 Mathematics  ·  Relations and Functions  ·  JEE

f: R to R defined by f(x) = x³ is:

Answer: Bijective.

  • A Injective but not surjective
  • B Surjective but not injective
  • C Bijective
  • D Neither

Correct answer: C. Bijective

Explanation: Injective: f(a)=f(b) ⟹ a³=b³ ⟹ a=b (cube root is unique in R). Surjective: for any y∈R, x=y<sup>1/3</sup> ∈ R satisfies f(x)=y (every real has a real cube root). Both injective and surjective ⟹ bijective. Answer: f(x)=x³ is bijective

Concept context

Ordered pairs, Cartesian products, types of relations and functions, domain and range. Foundation for calculus and Class 12 algebra.

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