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let f(x +p) =1 + { 2-3f(x) - 3(f(x))^2 - (f(x))^3}^1/3, for all x belongs to R,where p >0 then find period of f(x).

let f(x +p) =1 + { 2-3f(x) - 3(f(x))^2 - (f(x))^3}^1/3, for all x belongs to R,where p >0 then find period of f(x).

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1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans: 2p
f(x+p) = 1 + (2-3f(x)+3f(x)^{2}-f(x)^{3})^{\frac{1}{3}}
f(x+p) = 1 + (1+(1-f(x))^{3})^{\frac{1}{3}}
x\rightarrow x+p
f(x+p+p) = 1 + (1+(1-f(x+p))^{3})^{\frac{1}{3}}
1-f(x+p) = -(1+(1-f(x))^{3})^{\frac{1}{3}}
f(x+2p) = 1 + (1+(-(1+(1-f(x))^{3}))^{\frac{1}{3}}
f(x+2p) = 1-1+f(x)=f(x)
So, the time period of f(x) is 2p.
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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