# For real x,let then Option 1) is onto but not one-one Option 2) is one-one and onto Option 3) is neither one-one nor onto Option 4) is one-one but not  onto

As we learnt in

Onto function -

If  f:AB is such that each & every element in B is the image of atleast one element in A.Then it is Onto function.

- wherein

The range of f is equal to codomain of f.

One - One or Injective function -

A line parallel to x - axis cut the curve at most one point.

-

f(x) = x3 + 5x + 1

f'(x) = 3x2 + 5 > 0

Which is strictly increasing function so that it is one - one function.

For

So it is onto function.

Correct option is 2.

Option 1)

is onto but not one-one

This is an incorrect option.

Option 2)

is one-one and onto

This is the correct option.

Option 3)

is neither one-one nor onto

This is an incorrect option.

Option 4)

is one-one but not  onto

This is an incorrect option.

N

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