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Misc 18 - Let f be Signum Function, g be greatest integer - Composite funcions

Misc 18 - Chapter 1 Class 12 Relation and Functions - Part 2
Misc 18 - Chapter 1 Class 12 Relation and Functions - Part 3

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Misc 18 Let f: R → R be the Signum Function defined as 𝑓 𝑥﷯= 1 , 𝑥>0﷮&0, 𝑥=0﷮−1 , 𝑥<0﷯﷯ and g: R → R be the Greatest Integer Function given by g(x) = [x], where [x] is greatest integer less than or equal to x. Then does fog and gof coincide in (0, 1]? We have to find gof and fog in (0, 1] i.e. 0 < x ≤ 1 gof = g(f(x)) = [f(x)] = [1] = 1 fog = f(g(x)) = 𝑓 0﷯ , 0<𝑥<1﷮𝑓 1﷯, 𝑥=1﷯﷯ = 0, 0<𝑥<1﷮1, 𝑥=1﷯﷯ Hence gof = 1 & fog = 0, 0<𝑥<1﷮1, 𝑥=1﷯﷯ In gof , there is only one value, & in fog ,there are two values Hence, fog and gof do not coincide in (0, 1].

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.