Question:
If $f(x + 1) = x^2 - 3x + 2$, then f (x) is equal to:
If $f(x + 1) = x^2 - 3x + 2$, then f (x) is equal to:
Updated On: Jul 6, 2022
- $x^2 - 5x - 6$
- $x^2 + 5x - 6$
- $x^2 + 5x + 6$
- $x^2 - 5x + 6$
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The Correct Option is D
Solution and Explanation
Given function is :
$f (x + 1) = x^2 - 3x + 2$
This function is valid for all real values of x.
So, putting x - 1 in place of x, we get
$f (x) = f (x - 1 + 1)$
$\Rightarrow \, f (x) = (x - 1)^2 - 3(x - 1) + 2$
$\Rightarrow \, f (x) = x^2 - 2x + 1 - 3x + 3 + 2$
$f (x) = x^2 - 5x + 6$
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Notes on Relations and functions
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
