Answer :

False

In order to prove composition of functions is commutative we need to show


(fog)(x) = (gof)(x)


Let us suppose, f(x) = 2x, g(x) = 1 + x2


Now,


(fog)(x) = f(g(x)) = f(1+x2)


= 2(1+x2) = 2+2x2 (i)


(gof)(x) = g(f(x)) = g(2x)


= 1+(2x)2 = 1+4x2 (ii)


From (i) and (ii), we observe that


(fog)(x) ≠ (gof)(x)


Thus, composition of functions is not commutative.


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