If `f(a-x)=f(a+x) " and " f(b-x)=f(b+x)` for all real x, where `a, b ( – InterviewSolution

1.	If `f(a-x)=f(a+x) " and " f(b-x)=f(b+x)` for all real x, where `a, b (a gt b gt 0)` are constants, then prove that `f(x)` is a periodic function.
Answer» `f(x)=f(b+(x-b))` ` =f(b-(x-b))` `=f(2b-x)` `=f(a+(2b-x-a))` `=f(a-(2b-x-a))` `=f(2a-2b+x)` Hence, `f(x)` is periodic with period `2a-2b.`

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