Q59 of 70 Page 11

State True or False for the statements

The composition of functions is commutative.

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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