Question:
The graph of the function $y = f(x) $is symmetrical about the line $x = 2$, then
The graph of the function $y = f(x) $is symmetrical about the line $x = 2$, then
Updated On: Jul 5, 2022
- $ f (x + 2) =f (x-2) $
- $f (2 + x )= f (2 -x ) $
- $f (x ) = f ( - x) $
- $f (x) = -f (-x)$
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The Correct Option is B
Solution and Explanation
Since graph is symmetrical about the line $x = 2$
$\therefore \:\: f(2 + x) = f(2 - x)$.
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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}
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- Arrow Representation
