Engineering
Mathematics
Periodic Function
domain of function
Graphs Related Problems in Function
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?
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Solution
f(x) is symmetrical about the line x = 1
So,
f(1 – x) = f(1 + x) .................... (1)
f(x) is symmetrical about the line x = 2
So,
f(2 – x) = f(2 + x) .................... (2)
Replace x with 1 – x in equation (1) ,
f(1 – 1 + x) = f(1 + 1 – x)
f(x) = f(2 – x) ..........................(3)
From (2) and (3) ,
f(x) = f(2 + x)