(A) Since $f$ is a linear function,it can be represented as $f(x) = mx + c$. Given the points $(1, 1)$ and $(0, -1)$ belong to the function $f$,we hav

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(A) Since $f$ is a linear function,it can be represented as $f(x) = mx + c$. Given the points $(1, 1)$ and $(0, -1)$ belong to the function $f$,we have: $f(0) = m(0) + c = -1 \implies c = -1$. $f(1) = m(1) + c = 1 \implies m - 1 = 1 \implies m = 2$. Substituting $m = 2$ and $c = -1$ into the linear form,we get $f(x) = 2x - 1$.

Class 11 Mathematics Relations and Functions Different types of Function

Easy

Let $f = \{(1, 1), (2, 3), (0, -1), (-1, -3)\}$ be a linear function from $\mathbb{Z}$ into $\mathbb{Z}$. Find $f(x)$.

A
$f(x) = 2x - 1$
B
$f(x) = x + 1$
C
$f(x) = 3x - 2$
D
$f(x) = 2x + 1$

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Different types of Function

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Let $f = \{(1, 1), (2, 3), (0, -1), (-1, -3)\}$ be a linear function from $\mathbb{Z}$ into $\mathbb{Z}$. Find $f(x)$.

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