SATHEE: Limit Continuity and Differentiability 7 Question 11

Limit Continuity and Differentiability 7 Question 11

11. For $x \in R, f (x) = | \log 2 - \sin x |$ and $g (x) = f (f (x))$ , then

(a) $g$ is not differentiable at $x = 0$

(2016 Main)

(b) $g^{'} (0) = \cos (\log 2)$

(d) $g$ is differentiable at $x = 0$ and $g^{'} (0) = - \sin (\log 2)$

Show Answer

Answer:

Correct Answer: 11. (d)

Solution:

Here, $g$ is the inverse of $f (x)$ . $\Rightarrow$

$f \circ g (x) = x$

On differentiating w.r.t. $x$ , we get

$\begin{matrix} f^{'} g (x) \times g^{'} (x) = 1 \Rightarrow g^{'} (x) = \frac{1}{f^{'} (g (x))} \\ = \frac{1}{\frac{1}{1 + {g (x)}^{5}}} ∵ f^{'} (x) = \frac{1}{1 + x^{5}} \\ \Rightarrow g^{'} (x) = 1 + {g (x)}^{5} \end{matrix}$

Limit Continuity and Differentiability 7 Question 11

11. For $x \in R, f (x) = | \log 2 - \sin x |$ and $g (x) = f (f (x))$ , then

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Limit Continuity and Differentiability 7 Question 11

11. For x∈R,f(x)=|log⁡2−sin⁡x| and g(x)=f(f(x)), then

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

11. For $x \in R, f (x) = | \log 2 - \sin x |$ and $g (x) = f (f (x))$ , then