UPSC NDA I 2025 Mathematics Paper

Given,
The function is f(x)=px+q, a linear polynomial.
Since f(x)=px+q is linear with p≠0, it is one-one (injective): different x give different‌f(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 N. For f to be onto, its range must equal its codomain, but here:
{1,4,7,10}≠N
∴f is one-one but not onto.