If the graph of `y=f(x)` is symmetrical about the lines `x=1a n dx=2,` then which of the following is true? `f(x+1)=f(x)` (b) `f(x+3)=f(x)` `f(x+2)=f(x)` (d) None of these

Options

A. `f(x+1)=f(x)`
B. `f(x+3)=f(x)`
C. `f(x+2)=f(x)`
D. none of these

Answer

C

Explanation

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)`
` or f(1+x)=f(3+x) " [From (1)]" `
` or f(x) = f(2+x)`