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📐 Mathematics  ·  Relations and Functions  ·  JEE

If f: R to R satisfies f(x + y) = f(x) + f(y) and f(1) = 2, then f(n) for natural number n =

Answer: 2n.

  • A n
  • B
  • C 2<sup>n</sup>
  • D 2n

Correct answer: D. 2n

Explanation: Cauchy's functional equation: set y=1 repeatedly. f(2)=f(1)+f(1)=4, f(3)=f(2)+f(1)=6. By induction, f(n)=n·f(1). With f(1)=2: f(n)=n×2=2n. Answer: f(n) = 2n

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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