# The graph of the function  $\dpi{100} y=f\left ( x \right )$  is symmetrical about the line $\dpi{100} x=2$ ,then Option 1) $f\left ( x \right )= f\left ( -x \right )$ Option 2) $f\left (2+ x \right )= f\left ( 2-x \right )$ Option 3) $f\left ( x +2\right )= f\left ( x-2 \right )$ Option 4) $f\left ( x \right )=- f\left ( -x \right )$

N neha
H Himanshu

As we learnt in

Even Function -

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

- wherein

Since a graph symmetric about y-axis

means  x = 0 then it is even function and f(-x) = f(x)

$\therefore$    f(0 - x) = f(0 + x)     (b < z it is symmetric about v = 0 )

But in question it is symmetric about x = 2

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

Correct option is 3.

Option 1)

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

Option 2)

$f\left (2+ x \right )= f\left ( 2-x \right )$

Option 3)

$f\left ( x +2\right )= f\left ( x-2 \right )$

Option 4)

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

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