find period

vijay kharya

If a and b are two fixed positive integers such that f (a + x) = b + [b³ + 1-3b² (f (x) + 3b(f (x))²-(f (x))³]^1/3 for all real x then f (x) is periodic function with period

1. a

2. 2a

3. b

4. 2b

please try. rates assured for correct answer +explanation, or give ANY HINT/METHOD/CLUE

AIR 538 Asish

f(a+x) - b = -[(f(x)-b)³]^1/3(Simplifying RHS after taking +b to LHS)

[f(a+x)-b] = -[f(x) -b]

=> f(a+x) + f(x) = 2b .... 1

=> f(2a+x) + f(a+x) = 2b ...... 2

(2) - (1) we get

f(2a+x) - f(x) = 0

=> f(x+2a) = f(x)

so period= 2a

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