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Let $f=\{(1,1),(2,3),(0,-1),(-1,-3)\}$ be a function from $\mathrm{Z}$ to $\mathrm{Z}$ defined by $f(x)=\boldsymbol{a} x+\boldsymbol{b}$, for some integers $a, b$. Determine $a, b$.
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We have $f(x)=a x+b$, for $x=1, f(x)=1$,
$\therefore a+b=1 \quad \ldots (i)$
For $x=2, f(x)=3$,
$\therefore 3=a \times 2+b$ or $2 a+b=3 \quad \ldots (ii)$
subtracting eqn (ii) from (i) $a=2, b=-1$
$\therefore a+b=1 \quad \ldots (i)$
For $x=2, f(x)=3$,
$\therefore 3=a \times 2+b$ or $2 a+b=3 \quad \ldots (ii)$
subtracting eqn (ii) from (i) $a=2, b=-1$
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