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  • The number of points at which <img alt="\mathrm{g(x)=\frac{1}{1+\frac{2}{f(x)}}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bg%28x%29%3D%5Cfrac%7B1%7D%7B1&plus;%5Cfra

The number of points at which \mathrm{g(x)=\frac{1}{1+\frac{2}{f(x)}}} is not differentiable, where \mathrm{f(x)=\frac{1}{1+\frac{1}{x}}} is

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

\mathrm{f(x)=\frac{1}{1+\frac{1}{x}}=\frac{x}{x+1}} is not differentiable at \mathrm{x=0,-1}. Also, \mathrm{g(x)=\frac{1}{1+\frac{2}{f(x)}}=\frac{1}{1+\frac{2(x+1)}{x}}=\frac{x}{3 x+2}} Thus, the point where g(x) is not diiferentiable are \mathrm{x=0,-1}, \mathrm{\frac{-2}{3}}.

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Ajit Kumar Dubey

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