Question

Let f = { (1,2), (2,3), (0,1), (-1,-3) } be a linear function from Z to Z. Find f(x).

Answer 1

Let,

the linear function from Z into Z 

                                                 = f(x)=ax+bf(x)=ax+b

Given f(1)=1,

f(2)=3,

f(0)=−1 and

f(−1)=−3

Now f(1)=1⇒a+b=1

f(0)=−1⇒0+b=−1⇒b=−1

now by substituiting b=−1 in a+b=1

         by this, we will get we get a-1 =1 

                                                      ⇒a=1+1=2

now we have a = 2 and b= −1

Hence the linear function from Z into Z will be f(x)=2x−1

Answer 2

Hello friend
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let f(x) = ax + b

f(1) = 1 = a + b 

f(2) = 3 = 2a + b 

therefore , a = 2 and b = -1

f(x) = 2x - 1 
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Hope it will help u