IIT JEE , AIEEE Forum - Mathematics , Trignometry - given a composition of two functions ,how do you identify whther they are periodic??

pottermania1990

given a composition of two functions ,how do you identify whther they are periodic??

pottermania1990

pl. answer if any one knows

pottermania1990

can some experts help me

RyuAmakusa

I think f(g(x)) is periodic if range of g(x) = domain of f(x) and g(x) is continous and atleast one of them is periodic.

pottermania1990

can u specify with examples..

djdylan2000

Jus draw a graph and see if it repeats more or less.

RyuAmakusa

for example take f(x) = x³g(x)=sinx though f(x) is not periodic since g(x) is periodic f(g(x)) is periodic if we take g(f(x)) it will have values repeated but i doubt if it will be periodic

vineetnegi

if the iner fuction is periodic then comp is periodic irrespectiv e of outer one

if outer is periodic and iner is not

if inner has constant derivative

or satisfy the condition

g(x+h)-g(x)=constant for a value of h

like sin(4x-5)is periodic

tan(sinx) will have 2Pi as period

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