GUJCET 2026 Math Paper

Concept:A function is one-one if different inputs always give different outputs.It is onto if every element of the codomain has at least one pre-image.Explanation:Check one-one condition:$f(1)=\frac{1+1}{2}=1$$f(2)=\frac{2}{2}=1$Here, $f(1)=f(2)$ but $1\neq2$.So, $f$ is not one-one; it is many-one.Check onto condition:For any $y\in\mathbb{N}$, choose $n=2y$.Since $n$ is even, $f(2y)=\frac{2y}{2}=y$.Thus, every $y$ in the codomain has a pre-image.So, $f$ is onto.Therefore, $f$ is many-one and onto.Answer:Option C: Many-one and onto.