For real x,let f\left ( x \right )= x^{3}+5x+1 then

  • Option 1)

    f is onto R but not one-one

  • Option 2)

    f is one-one and onto R

  • Option 3)

    f is neither one-one nor onto R

  • Option 4)

    f is one-one but not  onto R

 

Answers (2)

As we learnt in

Onto function -

If  f:A\rightarrowB 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 x\epsilon R      f(x)\epsilon R

So it is onto function. 

Correct option is 2.

 

 


Option 1)

f is onto R but not one-one

This is an incorrect option.

Option 2)

f is one-one and onto R

This is the correct option.

Option 3)

f is neither one-one nor onto R

This is an incorrect option.

Option 4)

f is one-one but not  onto R

This is an incorrect option.

N neha

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