(A) Given the function $f = \{(1, 1), (2, 3), (0, -1), (-1, -3)\}$ defined by $f(x) = ax + b$.Using the point $(0, -1) \in f$,we have $f(0) = -1$.Subs

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(A) Given the function $f = \{(1, 1), (2, 3), (0, -1), (-1, -3)\}$ defined by $f(x) = ax + b$.Using the point $(0, -1) \in f$,we have $f(0) = -1$.Substituting $x = 0$ into $f(x) = ax + b$,we get $a(0) + b = -1$,which implies $b = -1$.Using the point $(1, 1) \in f$,we have $f(1) = 1$.Substituting $x = 1$ and $b = -1$ into $f(x) = ax + b$,we get $a(1) + (-1) = 1$.$a - 1 = 1 \Rightarrow a = 2$.Thus,the values are $a = 2$ and $b = -1$.

Class 12 Mathematics Relations and Functions Functional Equations

Medium

Let $f = \{(1, 1), (2, 3), (0, -1), (-1, -3)\}$ be a function from $\mathbb{Z}$ to $\mathbb{Z}$ defined by $f(x) = ax + b$ for some integers $a$ and $b$. Determine the values of $a$ and $b$.

A
$a = 2, b = -1$
B
$a = 1, b = 2$
C
$a = -2, b = 1$
D
$a = 2, b = 1$

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DifficultJEE MAIN 2025

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Let $f = \{(1, 1), (2, 3), (0, -1), (-1, -3)\}$ be a function from $\mathbb{Z}$ to $\mathbb{Z}$ defined by $f(x) = ax + b$ for some integers $a$ and $b$. Determine the values of $a$ and $b$.

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