Question

The graph of the function $y=f\left(x\right)$ is symmetrical about the line $x=2$. Then,

• A. $f(x+2)=f(x-2)$
• B. $f(2+x)=f(2-x)$
• C. $f\left(x\right)=f(-x)$
• D. $f\left(x\right)=-f(-x)$

Answer 1

The correct option is B $f(2+x)=f(2-x)$

If a function $h\left(x\right)$ is symmetrical about $yaxis(i.e.x=0)$, then we can write :

$h\left(x\right)=h(-x)$

It can also be written as :

$h(0+x)=h(0-x)$

$\therefore$ a function f(x) which is symmetrical about $x=2$, can be written as:

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