Answer :

TIP: One – One Function: – A function is said to be a one – one functions or an injection if different elements of A have different images in B.


So, is One – One function


a≠b


f(a)≠f(b) for all


f(a) = f(b)


a = b for all


Let, f1: R R and f2: R R are two functions given by


f1(x) = x


f2(x) = x


From above function it is clear that both are One – One functions


Now, f1×f2 : R Rgiven by


(f1×f2 )(x) = f1(x)×f2(x) = x2


(f1×f2 )(x) = x2


Also,


f(1) = 1 = f( – 1)


Therefore,


f is not One – One


f1×f2 : R R is not One – One function.


Hence Proved


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