plese answer the question with explanation...................................

The extremum of the codomain are 1 and 13. Thus the minimum value of f(x) is 1 and maximum is 13.
Also, we know that:
where m and M are the mimimum and maximum values of the function.
Since this equality holds in either of the case, f(x) = 1 between 3p and (3p+3)
and f(x) = 13 between 3q and 3q+3.
p²+q²is an odd integer implies that one of p & q is odd and the other is even.
So f(x) can be defined in 2 ways i.e. :

OR
.

Thus there are only 2 such functions and clearly, both have a period of 6since f(x+6) = f(x).
We know that for a periodic function f(x) with period p,
Thus,

At x = 3, the Left Hand Limit = k₁and Right Hand Limit = k₂
From the definition of f(x), either k₁ = 13k₂ or k₂ = 13k₁

Approved