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Question
Let f : R → R and g : R → R be defined by f(x) = x2 and g(x) = x + 1. Show that fog ≠ gof.
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Solution
Given, f : R → R and g : R → R.
So, the domains of f and g are the same.
(fog) (x) = f (g (x)) = f (x+1)= (x+1) 2 = x2+1+2
(gof) (x) = g (f (x)) = g (x2)=x2+1
So, fog ≠ gof
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