Q. 20

# Suppose f1</

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 non – zero functions given by

f1(x) = x3

f1(x) = x

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

Now, given by

Again,

defined by

f(x) = x2

Now,

f(1) = 1 = f( – 1)

Therefore,

f is not One – One

is not One – One function.

Hence it is not necessarily to be one – one function.

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