Let f= (1, 1), (2, 3), (0, -1), (-1, -3) be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a ,b.

Question

Let f= (1, 1), (2, 3), (0, -1), (-1, -3) be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a ,b. (A) 2, -1 (B) -2, 1 (C) 1, 2 (D) -2, -1

Tardigrade Admin · Accepted Answer

Given f(x) = ax+ b, for some integers a, b. When (1, 1) ∈ f ⇒ f(1) =1 ⇒ a + b = 1 ldots(i) When (2, 3) ∈ f ⇒ f(2) =3 ⇒ 2a + b = 3 ldots(ii) Solving (i) and (ii), we get a = 2, b = -1

Q. Let $f = {(1, 1), (2, 3), (0, - 1), (- 1, - 3)}$ be a function from $Z$ to $Z$ defined by $f (x) = a x + b$ , for some integers $a$ , $b$ . Determine $a, b$ .

$2$ , $- 1$

$- 2$ , $1$

$1$ , $2$

$- 2$ , $- 1$

Given $f (x) = a x + b$ , for some integers $a$ , $b$ .
When $(1, 1) \in f$
$\Rightarrow f (1) = 1$
$\Rightarrow a + b = 1 \dots (i)$
When $(2, 3) \in f$
$\Rightarrow f (2) = 3$
$\Rightarrow 2 a + b = 3 \dots (ii)$
Solving $(i)$ and $(ii)$ , we get
$a = 2$ , $b = - 1$

Q. Let f={(1,1),(2,3),(0,−1),(−1,−3)} be a function from Z to Z defined by f(x)=ax+b, for some integers a, b. Determine a,b.

2, −1

−2, 1

1, 2

−2, −1