Q. 17

Give examples of two one – one functions f1 and f2 from R to R such that f1 + f2 : R R, defined by (f1 + f2)(x) = f1(x) + f2(x) is not one – one.

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 be two functions given by (Examples)


f1(x) = x


f1(x) = – x


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


Now,


(f1 + f2)(x) = f1(x) + f2(x)


(f1 + f2)(x) = x – x


(f1 + f2)(x) = 0


Therefore,


f1 + f2 : R R is a function given by


(f1 + f2)(x) = 0


Since f1 + f2 is a constant function,


Hence it is not an One – One function.


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