Question

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

Answer 1

Hey There!!!

Here, we have f={(1,1),(2,3),(0,-1),(-1,-3)}

We are given that f is a linear function from Z into Z. This simply means that f(x) is a polynomial of degree 1.

Let f(x) = ax+b

All elements of the set f satisfy this equation.

Let us put (1,1).

That is, when x=1, f(x)=1

So, 1 = a + b -----(1)

Also, let us put (0,-1) there.

We have:-1 = a(0) + b

So, we have b = -1

Put b = -1 in equation (1), we have

1 = a - 1So, a = 2

Finally we have:

{f(x)=2x-1}}

We can easily see that all elements of set f satisfy the equation. So it is correct.

Hope it helps

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