The graph of f: R→ R defined by y = f(x) is symmetric with respect to x = a and x = b. Which of the following is true?

Given, f(a+x)=f(a−x)(a) f(2a−x)=f(a+(a−x))=f(a−(a−x))=f(x)     f(2a−x)=f(x)----i(b)        f(2a+x)=f(a+(a+x))=f(a−(a+x))=f(−x)∴ f(2a+x)=f(−x)----ii(c)  f(2b+x)=f(−x)       [from Eq. (i)] ………..(iii)(d)  From Eqs. (i) and (i), we get  f (2a + x) = f(2b + x)      ∴Period is(2b−2a)