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  • If the function f is defined by  <img alt="\mathrm{ f(x)=\frac{x}{1+|x|}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%20f%28x%29%3D%5Cfrac%7Bx%7D%7B1&plus;

If the function f is defined by  \mathrm{ f(x)=\frac{x}{1+|x|}}   then at what points is f differentiable?

Option: 1

everywhere


Option: 2

except at \mathrm{x= \pm 1}


Option: 3

except at x=0


Option: 4

except at \mathrm{ x=v~ or \pm 1 .}


Answers (1)

best_answer

We have

\mathrm{f(x)=\frac{x}{1+|x|}= \begin{cases}\frac{x}{1+x}, & x>0 \\ 0 & , x=0 \\ \frac{x}{1-x}, & x<0\end{cases}}

\mathrm{\therefore L f^{\prime}(0)=R f^{\prime}(0)=0} . So, f(x) is differentiable at x=0. Also, f(x) is differentiable at all other points. Hence, f(x) is everywhere differentiable.

Posted by

Devendra Khairwa

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