symmetric function

If f(x) is continous in R and is symmetrical abt the lines x=1 and x=2 then which of the following holds.

a)f(1+x)=f(x) b)f(x+3)=f(x)

c)f(x+2)=f(x) d)none of these.

pls explain.i know this will be a two liner but i am not getting ne.

1 Answers

106

Asish Mahapatra ·2009-10-30 02:14:07

it is symmetrical abt x=1

So f(1+x) = f(1-x) ... (i) this u can better understand from graph

similarly f(2+x) = f(2-x) ... (ii)

f(2+x) = f(1+(1+x)) = f(1-(x+1)) = f(-x)
f(2-x) = f(1-(x-1)) = f(1+x-1) = f(x)

So f(2+x) =f(x)

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