Question

Q34. Let f = {(1,1), (2,3), (0, –1), (–1, –3)} be a linear function from Z into 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: 

$\boxed{\textbf{f(x)=2x-1}}$


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

Hope it helps
Purva
Brainly Community

Answer 2

$\: \sf \: f \big(x \big) = ax + b$


$\sf \: 1 = a + \cancel{b} \: \: \: \: \: \: ........1$


$\sf \: 3 = 2a + \cancel{b} \: \: \: \: \: \: .......2$


$\sf \: + 2 = + a$


$\underline{\boxed{ \sf \: a = 2}}$


$\sf b = 1 - a$

$\sf \: = 1 - 2$


$\underline{ \boxed{ \sf = - 1}}$

$\underline{ \boxed{ \color{red} \sf \: f \bigg(x \bigg) = 2x - 1}}$

$\sf \: f \: \big(0\big) = 0 - 1 = - 1$