Question

Let $A=\{-1,1\}$ and $B=\{0,2\}$. If the function $f:A\to B$ defined by $f\left(x\right)=ax+b$ is an onto function? Find $a$ and $b$.

Answer 1

$A=\{-1,1\};B=\{0,2\}$
$f\left(x\right)=ax+b$
$f(-1)=a(-1)+b$
$0=-a+b$
$a-b=0\dots .\left(1\right)$
$f\left(1\right)=a\left(1\right)+b$
$2=a+b$
$a+b=2\dots .\left(2\right)$
Solving (1) and (2) we get
$$\begin{array}{cc}& a-b=0\\ & \underset{–}{a+b=2}\dots \left(1\right)\\ & \left(1\right)+\left(2\right)\Rightarrow 2a=2\\ & a=\frac{2}{2}=1\end{array}$$
Substitute $a=1$ in (1)
The value of $a=1$ and $b=1$