IIT JEE , AIEEE Forum - Mathematics , Differential Calculus - if f(a+x)=f(2a), then predict whether f(x) is periodic or not

umang

if periodic, find its period.

little_genius

f(x) is a constant fuction.so it is periodic whiose period is indeterminate>.............

umang

pls explain !!!

hash_include

'a' is a constant right?? if so, f(a+x) = f(2a) implies f(x) = f(2a) also.. implies constant function..
whose fundamental period is indeterminate..

umang

f(a+x) = f(2a) implies f(x) = f(2a)
i didnt get it
pls explain !!!

neeraj_agarwal_1990

f(a+x) = f(2a) is an identity...so we can put any value of x...

put x-->x-a..
so f(x) =f(2a) which means its constant.....i saw a question in which a constant function was marked as periodic...

ramkumar_november

yes f(x) is a constant function......

the speciality about constant function is that it is the only function which is periodic without any fundamental period.........

eistien

see f(a+x) is a constant f(2a) as for any value for x it has a constant value f(2a)

see for a constant function

f(x)=k

consider a T which is such that

f(T+x)=f(x)

but as f(x+ anything)=the same constant

thus there is no definite period it is undefined understood???

eistien

period can be any value so no fundamental period

Ask & Discuss Questions with Community & Experts