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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
Dear student yes it is true as let g(x) has period Tthen fog (x+T) = fog (x) hence fog(x) is also periodic woth period T
dear student, aruns answer is clearly incorrect.we know that the period of a function h(x) is the smallest positive value T such thath(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 :)))
Dear student Please refer the link below for further knowledgehttps://www.askiitians.com/iit-jee-algebra/set-relations-functions/functions/ Good Luck
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