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Is period of fogx always same as period of gx? Pls answer. I'm not getting it as true for all times

Is period of fogx always same as period of gx? Pls answer. I'm not getting it as true for all times

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Grade:12

3 Answers

Arun
25750 Points
4 years ago
Dear student
 
yes it is true
 
as let g(x) has period T
then fog (x+T) = fog (x)
 
hence fog(x) is also periodic woth period T
Aditya Gupta
2081 Points
4 years ago
dear student, aruns answer is clearly incorrect.
we know that the period of a function h(x) is the smallest positive value T such that
h(x+T)= h(x) for all x.
now let g(x)= sinx and f(x)= cosx.
clearly period of g(x) is 2pi.
but period of fog(x)= cos(sinx) is pi bcoz fog(x+pi)= cos(sin(x+pi))= cos( – sinx)= cos(sinx)= fog(x).
Hence, period of fog need not be same as period of g.
kindly approve :)))
Vikas TU
14149 Points
4 years ago
Dear student 
Please refer the link below for further knowledge
Good Luck 

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