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.

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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