Question

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

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

Hint:

Symmetry about:
\(x=0\) (y-axis): \(f(x)=f(-x)\) (even function)
\(x=a\): \(f(a+x)=f(a-x)\)

Answer 1

The Correct Option is B

Step 1: A graph is said to be symmetric about the vertical line \(x=a\) if for every point \((a+h, f(a+h))\), there exists a corresponding point \((a-h, f(a-h))\).
Step 2: This condition mathematically implies: \[ f(a+h)=f(a-h) \]
Step 3: Given that the line of symmetry is \(x=2\), substitute \(a=2\): \[ f(2+x)=f(2-x) \]
Step 4: Hence, the correct relation is: \[ \boxed{f(2+x)=f(2-x)} \]