Chapter 2, Problem 5RE

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

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

To determine

To find: The value of the provided function by substitution method.

Answer to Problem 5RE

Solution:

a. $f\left(2\right)=0$

Explanation of Solution

Given:

It is provided in the problem that the function $f\left(x\right)=\frac{x^2-4}{x^2}$.

Calculation:

a. For $f\left(2\right)$, substitute $x$ as 2. That is, $f\left(2\right)=\frac{{\left(2\right)}^2-4}{{\left(2\right)}^2}=\frac{4-4}{4}=0$.

To determine

To find: The value of the provided function by substitution method.

Answer to Problem 5RE

Solution:

b. $f\left(-2\right)=0$

Explanation of Solution

Given:

It is provided in the problem that the function $f\left(x\right)=\frac{x^2-4}{x^2}$.

Calculation:

b. For $f\left(-2\right)$, substitute $x$ as $-2$. That is, $f\left(-2\right)=\frac{{\left(-2\right)}^2-4}{{\left(2\right)}^2}=\frac{4-4}{4}=0$.

To determine

To find: The value of the provided function by substitution method.

Answer to Problem 5RE

Solution:

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

Explanation of Solution

Given:

It is provided in the problem that the function $f\left(x\right)=\frac{x^2-4}{x^2}$.

Calculation:

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

To determine

To find: The value of the provided function by substitution method.

Answer to Problem 5RE

Solution:

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

Explanation of Solution

Given:

It is provided in the problem that the function $f\left(x\right)=\frac{x^2-4}{x^2}$.

Calculation:

d. For $-f\left(x\right)$, multiply by $-1$. That is, $-f\left(x\right)=-\left(\frac{x^2-4}{x^2}\right)=\frac{4-x^2}{x^2}$.

To determine

To find: The value of the provided function by substitution method.

Answer to Problem 5RE

Solution:

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

Explanation of Solution

Given:

It is provided in the problem that the function $f\left(x\right)=\frac{x^2-4}{x^2}$.

Calculation:

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

To determine

To find: The value of the provided function by substitution method.

Answer to Problem 5RE

Solution:

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

Explanation of Solution

Given:

It is provided in the problem that the function $f\left(x\right)=\frac{x^2-4}{x^2}$.

Calculation:

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