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Miscellaneous
Misc 2 Deleted for CBSE Board 2023 Exams
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Misc. 4 Important
Misc 5
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Misc. 8 Important
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Misc 10 Important
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Misc 11 (ii)
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Misc 15
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Misc 17 (MCQ) Important
Misc 18 You are here
Misc 19 (MCQ) Important Deleted for CBSE Board 2023 Exams
Last updated at March 16, 2023 by Teachoo
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<1𝑓 1, 𝑥=1 = 0, 0<𝑥<11, 𝑥=1 Hence gof = 1 & fog = 0, 0<𝑥<11, 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].