First slide

Algebra of real valued functions

Question

If the graph of y =f(x) is symmetrical about the lines x = 1 and x = 2, then which of the following is true?

Moderate

A

$f (x + 1) = f (x)$
B

$f (x + 3) = f (x)$
C

$f (x + 2) = f (x)$
D

None of these

Solution

From the given data,
$f (1 - x) = f (1 + x) - - - (1)$
$and f (2 - x) = f (2 + x) - - - - - (2)$
$In (2), replacing x by 1 + x, we have$
$f (1 - x) = f (3 + x)$
$f (1 + x) = f (3 + x) [from 1]$
$or f (x) = f (2 + x)$

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