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Grade: 12th pass
        plese answer the question with explanation...................................
2 years ago

## Answers : (1)

Partha Math Expert - askIITians
askIITians Faculty
25 Points
							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 = k2From the definition of f(x), either k1 = 13k2 or k2 = 13k1

2 years ago
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