SATHEE: Limit Continuity and Differentiability 7 Question 23

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) $[0, \infty)$

(d) $(0, \infty)$

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Answer:

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

Solution:

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

$∴ g (x) = f [f (x)] = | | x - 2 | - 2 |$

When, $x > 2$

$\begin{aligned} g (x) = | (x - 2) - 2 | = | x - 4 | = x - 4 \\ ∴ & g^{'} (x) = 1 when x > 2 \end{aligned}$

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Limit Continuity and Differentiability 7 Question 23

23. The set of all points, where the function f(x)=x1+|x| is differentiable, is

Answer:

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