Graph of function y = f(x) is symmetrical about line x = 2 , then

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1.Relation and Function

hard

The graph of the function $y = f(x)$ is symmetrical about the line $x = 2$, then

A

$f(x) = - f( - x)$

B

$f(2 + x) = f(2 - x)$

C

$f(x) = f( - x)$

D

$f(x + 2) = f(x - 2)$

(AIEEE-2004)

Solution

(b) $f(x) = f( – x) \Rightarrow f(0 + x) = f(0 – x)$ is symmetrical about $x = 0$.

$\therefore $ $f(2 + x) = f(2 – x)$ is symmetrical about $x = 2$.

Standard 12

Mathematics

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