I A Maron Solutions for Chapter: Introduction to Mathematical Analysis, Exercise 3: Investigation of Functions

Find the greatest value of the function $f\left(x\right)=\frac{2}{\sqrt{2x^2-4x+3}}.$

Identify whether the given function is even or odd :
 $f\left(x\right)=\sqrt[3]{(1-x{)}^2}+\sqrt[3]{(1+x{)}^2}$

Identify whether the given function is even or odd :
$f\left(x\right)=x^2-\left|x\right|$

Identify whether the given function is even or odd :
$f\left(x\right)=x{\sin }^{2}x-x^3$ 

Identify whether the given function is even or odd :
$f\left(x\right)=\frac{{\left(1+2^x\right)}^2}{2^x}$  

Find the period for the following function :
 $f\left(x\right)=\arctan \left(\tan x\right)$

Find the period for each of the following functions :
$f\left(x\right)=2\cos \frac{x-\pi }{3}$

Prove that the functions $f\left(x\right)=x+\sin x$ is non-periodic.