MathDB

Let be a function

f:\mathbb{R}\longrightarrow\mathbb{R}

such that: \text{(i)} f(0)=0 \text{(ii)} f'(x)\neq 0, \forall x\in\mathbb{R} \text{(iii)} \left. f''\right|_{\mathbb{R}}\text{ exists and it's continuous}
Demonstrate that the function

g:\mathbb{R}\longrightarrow\mathbb{R}

defined as

g(x)=\left\{\begin{matrix}\cos\frac{1}{f(x)},&emsp; x\neq 0\\ 0,&emsp; x=0\end{matrix}\right.

is primitivable.

Problem Statement