Amit M Agarwal Solutions for Chapter: Continuity and Differentiability, Exercise 3: Target Exercise 6.3

Let $f\left(x\right)=\left|x\right|+\left|\sin x\right|, x\in \left(-\frac{\pi }{2}, \frac{3\pi }{2}\right)$. Then $f$ is

If $f\left(x\right)$ is periodic function, then:

If $f\left(x\right)=\left[{\sin }^{2}x\right]$, (where$\left[.\right]$ denotes the greatest integer function), then

If $4x+3\left|y\right|=5y$, then $y$ as a function of $x$ is:

Let $g\left(x\right)$ be a polynomial of degree one and $f\left(x\right)$ be a function defined by $f\left(x\right)=\left\{\begin{array}{ll}g\left(x\right),& x\le 0\\ {\left(\frac{1+x}{2+x}\right)}^{\frac{1}{x}},& x>0\end{array}\right.$.

If $f\left(x\right)$ is continuous at $x=0$ and $f(-1)=f\text{'}\left(1\right)$, then $g\left(x\right)$ is equal to