Example 16 Find gof and fog, if f : R → R and g : R → R are given by f (x) = cos x and g (x) = 3x2. Show that gof ≠ fog. f(x) = cos x , g(x) = 3x2 Hence, gof ≠ fog. f(x) = cos x f(g(x)) = cos g(x) fog(x) = cos (3x2) g(x) = 3x2 g(f(x)) = 3 f(x)2 gof (x) = 3 cos2 x

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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