Chapter 2.1, Problem 68AYU

To determine

To find: $(f+g)\left(x\right)$, for the functions $f(x)=\left|x\right|$ and $g\left(x\right)=x$ and also the domain.

Answer to Problem 68AYU

$(f+g)\left(x\right)=\left|x\right|+x$; Domain $=$ All real numbers

Explanation of Solution

Given:

The function $f\left(x\right)=\left|x\right|$, $g\left(x\right)=x$

Calculation:

$(f+g)\left(x\right)= f\left(x\right)+g\left(x\right)$

$=\left|x\right|+x$

Domain $=$ All real numbers

To determine

To find: $\left(f-g\right)\left(x\right)$, for the functions $f(x)=\left|x\right|$ and $g\left(x\right)=x$ and also the domain.

Answer to Problem 68AYU

$\left(f-g\right)\left(x\right)=\left|x\right|-x$; Domain $=$ All real numbers

Explanation of Solution

Given:

The function $f\left(x\right)=\left|x\right|$, $g\left(x\right)=x$

Calculation:

$(f-g)\left(x\right)= f\left(x\right)-g\left(x\right)$

$=\left|x\right|-x$

Domain $=$ All real numbers

To determine

To find: $\left(f.g\right)\left(x\right)$, for the functions $f(x)=\left|x\right|$ and $g\left(x\right)=x$ and also the domain.

Answer to Problem 68AYU

$\left(f.g\right)\left(x\right)=\left|x\right|\cdot \left(x\right)$; Domain $=$ All real numbers

Explanation of Solution

Given:

The function $f\left(x\right)=\left|x\right|$, $g\left(x\right)=x$

Calculation:

$\left(f.g\right)\left(x\right)=f\left(x\right)\cdot g\left(x\right)$

$=\left|x\right|\cdot \left(x\right)$

$=\pm x²$

Domain $=$ All real numbers

To determine

To find: $\left(\frac{f}{g}\right)\left(x\right)$, for the functions $f(x)=\left|x\right|$ and $g\left(x\right)=x$ and also the domain.

Answer to Problem 68AYU

$\left(\frac{f}{g}\right)\left(x\right)=\frac{\left|x\right|}{x}$; Domain $=\left\{x\right|x\ne \text{ 0}\}$

Explanation of Solution

Given:

The function $f\left(x\right)=\left|x\right|$, $g\left(x\right)=x$

Calculation:

$\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$

$=\frac{\left|x\right|}{x}$

Domain $=\left\{x|x\ne \text{ 0}\right\}$

To determine

To find: $(f+g)\left(3\right)$, for the functions $f(x)=\left|x\right|$ and $g\left(x\right)=x$ and also the domain.

Answer to Problem 68AYU

$(f+g)\left(3\right)=6$

Explanation of Solution

Given:

The function $f\left(x\right)=\left|x\right|$, $g\left(x\right)=x$

Calculation:

$(f+g)\left(3\right)=\left|x\right|+x$

$=\left|3\right|+3$

$=3+\text{ 3}$

$=6$

To determine

To find: $\left(f-g\right)\left(4\right)$, for the functions $f(x)=\left|x\right|$ and $g\left(x\right)=x$ and also the domain.

Answer to Problem 68AYU

$\left(f-g\right)\left(4\right)=0$

Explanation of Solution

Given:

The function $f\left(x\right)=\left|x\right|$, $g\left(x\right)=x$

Calculation:

$(f-g)\left(4\right)=\left|x\right|-x$

$=\left|4\right|-\text{ 4}$

$=4-\text{ 4}$

$=\text{ 0}$

To determine

To find: $\left(f.g\right)\left(2\right)$, for the functions $f(x)=\left|x\right|$ and $g\left(x\right)=x$ and also the domain.

Answer to Problem 68AYU

$\left(f.g\right)\left(2\right)=4$

Explanation of Solution

Given:

The function $f\left(x\right)=\left|x\right|$, $g\left(x\right)=x$

Calculation:

$\left(f.g\right)\left(2\right)=\left|x\right|\cdot \left(x\right)$

$=\left|2\right|\cdot \text{ 2}$

$=\text{ 2 }\cdot \text{ 2}$

$=\text{ 4}$

To determine

To find: $\left(\frac{f}{g}\right)\left(1\right)$, for the functions $f(x)=\left|x\right|$ and $g\left(x\right)=x$ and also the domain.

Answer to Problem 68AYU

$\left(\frac{f}{g}\right)\left(1\right)=1$

Explanation of Solution

Given:

The function $f\left(x\right)=\left|x\right|$, $g\left(x\right)=x$

Calculation:

$\left(\frac{f}{g}\right)\left(1\right)=\frac{\left|x\right|}{x}$

$=\frac{\left|1\right|}{1}$

$=\frac{1}{1}$

$=1$