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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(x2)
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B
f(2+x)=f(2x)
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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 $$f(2 + x) = f(2 - x)$$
If a function $$h(x)$$ is symmetrical about $$y \,axis(i.e.\,x=0)$$, then we can write :
$$h(x)=h(-x)$$
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:
$$f(2+x)=f(2-x)$$

Mathematics

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