Question

Let $f:Z\to Z$ and $g:Z\to Z$ be functions defined by $f=\left\{\right(n,n^2):n\in Z\}$ and, $g:\left\{\right(n,|n{|}^2):n\in Z\}$. Then, $f=g$.

• A. True
• B. False

Answer 1

The correct option is A True

Domain of f = Domain of g = Z and,

Co-domain of f = Co-domain of g = Z

We have, $f\left(n\right)=n^2$ and $g\left(n\right)=|n{|}^2=n^2$

$\therefore f\left(n\right)=g\left(n\right)$ for all $n\in Z$.

Hence, $f=g$.