Chapter 3.1, Problem 19E

a)

To determine

The domain and range of the given function of a real variable and also find whether the function is one-to-one and whether it is onto for the following cases.

$f:\text{R}\to \text{R}$ defined by $f\left(x\right)=x^3$

b)

To determine

The domain and range of the given function of a real variable and also find whether the function is one-to-one and whether it is onto for the following cases.

$g:\text{R}\to \text{R}$ defined by $g\left(x\right)=x\left|x\right|$

c)

To determine

The domain and range of the given function of a real variable and also find whether the function is one-to-one and whether it is onto for the following cases.

$\beta :\left(\frac{4}{3},\infty \right)\to \text{R}$ defined by $\beta \left(x\right)={\log }_2\left(3x-4\right)$

d)

To determine

The domain and range of the given function of a real variable and also find whether the function is one-to-one and whether it is onto for the following cases.

$f:\text{R}\to \text{R}$ defined by $f\left(x\right)=2^{x-1}+3$