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

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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