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  • Confused! kindly explain, - Sets, Relations and Functions - JEE Main-3

Which of the functions f(x) will be one - one functions if f{}'\left ( x \right ) is given .

  • Option 1)

    {f}'\left ( x \right )=\sin x\: ,\: x\equiv R

     

     

     

  • Option 2)

    {f}'\left ( x \right )=e^{x}\: ,\: x\equiv R

  • Option 3)

    {f}'\left ( x \right )=ln\,\: x\: ,\: x\equiv R^{+}

  • Option 4)

    {f}'\left ( x \right )=\cos x\: ,\: x\equiv R

 

Answers (1)

best_answer

As we learned 

 

proof of one-one -

Increasing or decreasing

i.e. Monotonous

- wherein

\frac{dy}{dx}> 0

or   \frac{dy}{dx}< 0

in the domain.

 

 

when {f}'=e^{x}> 0

Thus f(x) is an increasing function. So it is a one one function.

 


Option 1)

{f}'\left ( x \right )=\sin x\: ,\: x\equiv R

 

 

 

Option 2)

{f}'\left ( x \right )=e^{x}\: ,\: x\equiv R

Option 3)

{f}'\left ( x \right )=ln\,\: x\: ,\: x\equiv R^{+}

Option 4)

{f}'\left ( x \right )=\cos x\: ,\: x\equiv R

Posted by

Himanshu

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