Q. 105.0( 1 Vote )

# Mark the correct alternative in each of the following:

The function f : [0, ∞) → R given by f(x) is

A. one-one and onto

B. one-one but not onto

C. onto but not one-one

D. neither one-one nor onto

Answer :

Given that f: [0, ∞) → R where

Let f(x) = f(y)

⇒ xy + x = xy + y

⇒ x = y

So, f is one-one.

Now, y = f(x)

⇒ xy + y = x

⇒ y = x – xy

Here, y≠1 i.e. y ϵ R.

So, f is not onto.

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