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:
- Given, $f(x)=|x-2|$
$\therefore \quad g(x)=f[f(x)]=|| x-2|-2|$
When, $\quad x>2$
$$ \begin{array}{rlrl} & & g(x)=|(x-2)-2|=|x-4|=x-4 \\ \therefore & g^{\prime}(x)=1 \text { when } x>2 \end{array} $$
