Question:
Let $f = \{ (1,1),(2,4),(0,- 2),(-1,- 5) \}$ be a linear function from $ Z $ into $ Z $ . Then, $ f (x) $ is
Let $f = \{ (1,1),(2,4),(0,- 2),(-1,- 5) \}$ be a linear function from $ Z $ into $ Z $ . Then, $ f (x) $ is
Updated On: Jun 14, 2022
- $ f(x) = 3x - 2 $
- $ f(x) = 6x - 8 $
- $ f(x) = 5x - 2 $
- $ f(x) = 7x + 2 $
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The Correct Option is A
Solution and Explanation
$f=\left\{\left(1, 1\right), \left(2,4\right), \left(0, -2\right), \left(-1,-5\right)\right\}$
Let the linear function is,
$y=mx+c \ldots\left(i\right)$
Then, at $\left(1, 1\right), 1=m+c \ldots\left(ii\right)$
at $\left(0, -2\right), -2=c$,
then $m=3$
Hence, the linear expression becomes
$y=f \left(x\right)=3x-2$
Let the linear function is,
$y=mx+c \ldots\left(i\right)$
Then, at $\left(1, 1\right), 1=m+c \ldots\left(ii\right)$
at $\left(0, -2\right), -2=c$,
then $m=3$
Hence, the linear expression becomes
$y=f \left(x\right)=3x-2$
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Concepts Used:
Relations and functions
A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.
Representation of Relation and Function
Relations and functions can be represented in different forms such as arrow representation, algebraic form, set-builder form, graphically, roster form, and tabular form. Define a function f: A = {1, 2, 3} → B = {1, 4, 9} such that f(1) = 1, f(2) = 4, f(3) = 9. Now, represent this function in different forms.
- Set-builder form - {(x, y): f(x) = y2, x ∈ A, y ∈ B}
- Roster form - {(1, 1), (2, 4), (3, 9)}
- Arrow Representation
