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

English

Gujarati

Hindi

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

Share

Similar Questions

Domain of the function $f(x) = {\sin ^{ – 1}}\left( {\frac{{2 – |x|}}{4}} \right) + {\cos ^{ – 1}}\left( {\frac{{2 – |x|}}{4}} \right) + {\tan ^{ – 1}}\left( {\frac{{2 – |x|}}{4}} \right)$ is

normal

Let $f(x) = {\cos ^{ – 1}}\left( {\frac{{2x}}{{1 + {x^2}}}} \right) + {\sin ^{ – 1}}\left( {\frac{{1 – {x^2}}}{{1 + {x^2}}}} \right)$ then the value of $f(1) + f(2)$, is –

normal

Show that none of the operations given above has identity.

normal

If $f(a) = a^2 + a+ 1$ , then number of solutions of equation $f(a^2) = 3f(a)$ is

normal

Let $x$ denote the total number of one-one functions from a set $A$ with $3$ elements to a set $B$ with $5$ elements and $y$ denote the total number of one-one functions from the set $A$ to the set $A \times B$. Then …… .

medium

(JEE MAIN-2021)