Consider the following statements:
I. f is one-one function.
II. f is onto function if the codomain is the set of natural numbers.
Which of the statements given above is/are correct?

Question

Question

Consider the following for the two (02) items that follow:
Let f = {(1, 1), (2, 4), (3, 7), (4, 10)}

This question was previously asked in

NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)

Answer 1

Calculation:

Given,

The function is \(f(x)=px+q\), a linear polynomial.

Since \(f(x)=px+q\) is linear with \(p\neq0\), it is one-one (injective): different \(x\) give different \(f(x)\).

The actual outputs given are \(\{1,4,7,10\}\), so the range of \(f\) is \(\{1,4,7,10\}\).

The codomain is the set of natural numbers \(\mathbb{N}\). For \(f\) to be onto, its range must equal its codomain, but here:

\(\{1,4,7,10\}\neq\mathbb{N}\)

∴ f is one-one but not onto.

Hence, the correct answer is Option 1.

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