Q. 7 B3.9( 36 Votes )

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.

f : R R defined by f (x) = 1 + x2

Answer :

It is given that f : R R defined by f (x) = 1 + x2

Let x1, x2ϵ R such that f(x1) = f(x2)



Now, f(1) = f(-1) = 2


f(x1) = f(x2) which does means that x1 = x2


f is not one one


Now consider an element -2 in co- domain R.


We can see that f(x) = 1 + x2 is always positive.


there does not exist any x in domain R such that f(x) = -2


F is not onto.


Therefore, function f is neither one-one nor onto.


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