Let A = –1, 1 and B = 0, 2 . If the function f: A → B defined by … - Vidyadip

Question

Let A = {–1, 1} and B = {0, 2}. If the function f: A → B defined by f(x) = ax + b is an onto function? Find a and b

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Answer

$A=\{-1,1\} ; B=\{0,2\}$
$f(x)=a x+b$
$f(-1)=a(-1)+b$
$0=-a+b$
$a-b=0 \ldots(1)$
$f(1)=a(1)+b$
$2=a+b$
$a+b=2 \ldots(2)$
Solving (1) and (2) we get
$a-b=0$
$a+b=2$
$(1)+(2) \Rightarrow 2 a=2$
$a=\frac{2}{2}=1$
Substitute $a =1$ in (1)
The value of $a=1$ and $b=1$

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