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Q.
Let $f= \{(1, 1), (2, 3), (0, -1), (-1, -3)\}$ be a function from $Z$ to $Z$ defined by $f(x) = ax + b$, for some integers $a$, $b$. Determine $a ,b$.
Relations and Functions
Solution:
Given $f(x) = ax+ b$, for some integers $a$, $b$.
When $(1, 1) \in f$
$\Rightarrow f(1) =1$
$\Rightarrow a + b = 1 \quad \ldots(i)$
When $(2, 3) \in f$
$\Rightarrow f(2) =3$
$\Rightarrow 2a + b = 3 \quad \ldots(ii)$
Solving $(i)$ and $(ii)$, we get
$a = 2$, $b = -1$