Chapter 2, Problem 3RE

In Problems 3-5, find the following for each function.

(a) $f\left(2\right)$

(b) $f\left(-2\right)$

(c) $f\left(-x\right)$

(d) $-f\left(x\right)$

(e) $f\left(x-\text{ 2}\right)$

(f) $f\left(2x\right)$

$f\left(x\right)\text{ = }\frac{3x}{x^2-1}$

To determine

The value of the provided function by substitution method.

Answer to Problem 3RE

Solution:

a. $f\left(2\right)=2$

Explanation of Solution

Given:

It is provided in the problem that the function $f\left(x\right)=\frac{3x}{x^2-1}$.

Calculation:

a. For $f\left(2\right)$, substitute $x$ as 2. That is , $f\left(2\right)=\frac{3\left(2\right)}{{\left(2\right)}^2-1}=\frac{6}{4-1}=\frac{6}{3}=2$.

To determine

The value of the provided function by substitution method.

Answer to Problem 3RE

Solution:

b. $f\left(-2\right)=-2$

Explanation of Solution

Given:

It is provided in the problem that the function $f\left(x\right)=\frac{3x}{x^2-1}$.

Calculation:

b. For $f\left(-2\right)$, substitute $x$ as $-2$. That is , $f\left(-2\right)=\frac{3\left(-2\right)}{{\left(-2\right)}^2-1}=\frac{-6}{4-1}=\frac{-6}{3}=-2$.

To determine

The value of the provided function by substitution method.

Answer to Problem 3RE

Solution:

c. $f\left(-x\right)=\frac{-3x}{x^2-1}$

Explanation of Solution

Given:

It is provided in the problem that the function $f\left(x\right)=\frac{3x}{x^2-1}$.

Calculation:

c. For $f\left(-x\right)$, substitute $x$ as $-x$. That is , $f\left(-x\right)=\frac{3\left(-x\right)}{{\left(-x\right)}^2-1}=\frac{-3x}{x^2-1}$.

To determine

The value of the provided function by substitution method.

Answer to Problem 3RE

Solution:

d. $-f\left(x\right)=\frac{-3x}{x^2-1}$

Explanation of Solution

Given:

It is provided in the problem that the function $f\left(x\right)=\frac{3x}{x^2-1}$.

Calculation:

d. For $-f\left(x\right)$, multiply by $-1$. That is , $-f\left(x\right)=-\left(\frac{3x}{x^2-1}\right)=\frac{-3x}{x^2-1}$.

To determine

The value of the provided function by substitution method.

Answer to Problem 3RE

Solution:

e. $f\left(x-2\right)=\frac{3\left(x-2\right)}{\left(x-3\right)\left(x-1\right)}$

Explanation of Solution

Given:

It is provided in the problem that the function $f\left(x\right)=\frac{3x}{x^2-1}$.

Calculation:

e. For $f\left(x-2\right)$, substitute $x$ as $x-2$. That is , $f\left(x-2\right)=\frac{3\left(x-2\right)}{{\left(x-2\right)}^2-1}=\frac{3x-6}{x^2-4x+4-1}=\frac{3x-6}{x^2-4x+3}=\frac{3\left(x-2\right)}{\left(x-3\right)\left(x-1\right)}$.

To determine

The value of the provided function by substitution method.

Answer to Problem 3RE

Solution:

f. $f\left(2x\right)=\frac{6x}{4x^2-1}$

Explanation of Solution

Given:

It is provided in the problem that the function $f\left(x\right)=\frac{3x}{x^2-1}$.

Calculation:

f. For $f\left(2x\right)$, substitute $x$ as $2x$. That is , $f\left(2x\right)=\frac{3\left(2x\right)}{{\left(2x\right)}^2-1}=\frac{6x}{4x^2-1}$.