Let f = {(1,1),(2,3),(0,-1),(-1,-3)} be linear …
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Posted by Sanchit Garg 8 years, 5 months ago
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Rasmi Rv 8 years, 5 months ago
Let the linear function from Z into Z be {tex}f\left( x \right) =ax+b{/tex}
Given {tex}f\left( 1 \right) =1,f\left( 2 \right) =3,f\left( 0 \right) =-1,f\left( -1 \right) =-3{/tex}
Now {tex}f\left( 1 \right) =1\Rightarrow a+b=1\\ f\left( 0 \right) =-1\Rightarrow 0+b=-1\Rightarrow b=-1{/tex}
Substituting {tex}b=-1{/tex} in a+b=1 we get a-1 =1 {tex}\Rightarrow{/tex}a=1+1=2
So we have a = 2 and {tex}b=-1{/tex}
Hence the linear function from Z into Z is {tex}f\left( x \right) =2x-1{/tex}
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