Let A = {−1, 0, 1, 2}, B = {−4, −2, 0, 2} and f,


Let $A=\{-1,0,1,2\}, B=\{-4,-2,0,2\}$ and $t, g: A \rightarrow B$ be functions defined by $f(x)=x^{2}-x, x \in \mathrm{A}$ and $g(x)=2\left|x-\frac{1}{2}\right|-1, x \in A$. Are $f$ and $g$ equal?

Justify your answer. (Hint: One may note that two function $f: A \rightarrow B$ and $g: A \rightarrow B$ such that $f(a)=g(a) \& m n F o r E ; a \in A$, are called equal functions).


It is given that A = {−1, 0, 1, 2}, B = {−4, −2, 0, 2}.

Also, it is given that $f, g: A \rightarrow B$ are defined by $f(x)=x^{2}-x, x \in A$ and $g(x)=2\left|x-\frac{1}{2}\right|-1, x \in A$.

It is observed that:



$\Rightarrow f(-1)=g(-1)$



$\Rightarrow f(0)=g(0)$



$\Rightarrow f(1)=g(1)$



$\Rightarrow f(2)=g(2)$

$\therefore f(a)=g(a) \forall a \in A$

Hence, the functions and g are equal.



Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now