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Question

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

A
f ( x+2) = f (x - 2)
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B
f (2 + x) =f (2 - x)
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C
f(x) = f(-x)
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D
f(x) = - f(-x)
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Solution

The correct option is B f (2 + x) =f (2 - x)
As the graph of f is symmetrical about x=2,the graph of f to the left of x=2 is same as the graph of f to the right of x=2.If (2x, y) is a point on the graph, then (2+x, y) is also a point on the graph.The functional value at (2x) is same as that of functional value at (2+x) .f(2 + x) = f(2 x)

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