Assertion (A): A function f: N → N given by f ( x )= x^3+2, ∀ x ∈ N is one-one but not onto. Reason (R): Since ∀ y ∈ N (Codomain), there does not…

Assertion (A): A function $\displaystyle \mathrm{f}: \mathrm{N} \rightarrow \mathrm{N}$ given by $\displaystyle \mathrm{f}(\mathrm{x})=\mathrm{x}^{3}+2, \forall \mathrm{x} \in \mathrm{N}$ is one-one but not onto. Reason (R) : Since $\displaystyle \forall \mathrm{y} \in \mathrm{N}$ (Codomain), there does not exist $\displaystyle \mathrm{x}=(\mathrm{y}-2)^{1 / 3}$ in N (Domain) such that $\displaystyle \mathrm{f}(\mathrm{x})=\mathrm{x}^{3}+2=\mathrm{y}$.