Question

If $A=\{x|-1\le x\le 1\}=B,$ then find out which function is one -one , into or one-one onto defined from A to B
$f\left(x\right)=\frac{x}{2}$

Answer 1

Function defined from A to B .
$f:A\to B,f\left(x\right)=\frac{x}{2}$
Let$x_1,x_2\in A$
If $f\left(x_1\right)=f\left(x_2\right)\Rightarrow \frac{x_1}{2}=\frac{x_2}{2}$
$\Rightarrow x_1=x_2\forall x_1,x_2\in A$
$=\{x:\frac{-1}{2}\le x\le \frac{1}{2}\}$