Grade 12IIT JEE Entrance Exam
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
3 Answers
Arun
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
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
Dear student
Please refer the link below for further knowledge
Good Luck
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