The graph of the function  y=f\left ( x \right )  is symmetrical about the line 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 )

 

Answers (2)
N neha
H Himanshu

As we learnt in

Even Function -

f(-x)= f(x)

- wherein

Symmetric about Y - axis

 

 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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