The Total solution for NCERT class 6-12
Let f: R → R and g: R → R bedefined by f(x) = x2 and g(x) = x + 1.Show that fog ≠ gof.
Givenf: R → R and g: R → R.So, the domains of f and g are the same.
Consider(fog) (x) = f (g (x))
= f (x + 1)= (x + 1)2
= x2 +1 + 2x
Again consider(gof) (x) = g (f (x))
= g (x2)= x2 + 1
So, fog ≠ gof