Limit Continuity and Differentiability 7 Question 23

23. The set of all points, where the function $f(x)=\frac{x}{1+|x|}$ is differentiable, is

(1987, 2M)

(a) $(-\infty, \infty)$

(b) $[0, \infty)$

(c) $(-\infty, 0) \cup(0, \infty)$

(d) $(0, \infty)$

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Answer:

Correct Answer: 23. $(a, d)$

Solution:

  1. Given, $f(x)=|x-2|$

$\therefore \quad g(x)=f[f(x)]=|| x-2|-2|$

When, $\quad x>2$

$$ \begin{array}{rlrl} & & g(x)=|(x-2)-2|=|x-4|=x-4 \\ \therefore & g^{\prime}(x)=1 \text { when } x>2 \end{array} $$



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