Verified Solution • 2025–26 Session moderate

QJEEM21Mac599: JEE Main 2021 Mathematics - Class 11 JEEM21Mac599 Solution: Let f, g : N N such that f(n + 1) = f(n) + f(1) n N and g be…

Let f, g : N →\to N such that f(n + 1) = f(n) + f(1) ∀\forall n ∈\in N and g be any arbitrary function. Which of the following statements is NOT true?

Multiple Choice Options

  • A If g is onto, then fog is one-one
  • B f is one-one
  • C If f is onto, then f(n) = n ∀\forall n ∈\in N
  • D If fog is one-one, then g is one-one

Step-by-Step Verified Solution

f(n+1)=f(n)+1f(n + 1) = f(n) + 1

f(2)=2f(1)f(2) = 2f(1)

f(3)=3f(1)f(3) = 3f(1)

f(4)=4f(1)f(4) = 4f(1)

.....

f(n)=nf(1)f(n) = nf(1)

f(x)f(x) is one-one

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