Question

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

Answer:

Since f is a linear function.

Let f(x)=mx+c

  x y  y=mx+c (1,1) 1  1  1=m×1+c⇒1=m+c (2,3) 2 3 3=m×2+c⇒3=2m+c

Solving m+c=1     .....(1)

2m+c=3       .......(2)

Equation (2)−(1)

⇒2m+c−(m+c)=3−1

⇒2m+c−m−c=2

⇒m=2

Put m=2 in (1)

m+c=1

⇒2+c=1

⇒c=1−2=−1

So,f(x)=mx+c=2x−1

Answer 2

Answer:

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