Solve this


Let $f=\{(0,-5),(1,-2),(3,4),(4,7)\}$ be a linear function from $Z$ into $Z$. 

Write an expression for f.



Given that: $f=\{(0,-5),(1,-2),(3,4),(4,7)\}$ be a function from $Z$ to $Z$ defined

by linear function.

We know that, linear functions are of the form y = mx + b

Let f(x) = ax + b, for some integers a, b

Here, $(0,-5) \in f$

$\Rightarrow \mathrm{f}(0)=-5$

$\Rightarrow \mathrm{a}(0)+\mathrm{b}=-5$

$\Rightarrow \mathrm{b}=-5 \ldots(\mathrm{i})$

Similarly, $(1,-2) \in f$

$\Rightarrow f(1)=-2$

$\Rightarrow a(1)+b=-2$

$\Rightarrow a+b=-2$

$\Rightarrow a+(-5)=-2[$ from (i) $]$

$\Rightarrow a=-2+5$

$\Rightarrow a=3$

$\therefore f(x)=a x+b$

$=3 x+(-5)$

$f(x)=3 x-5$


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