Chapter 2, Problem 7RE

a.

To determine

To find the value of $f\left(2\right)$ .

Answer to Problem 7RE

  $f\left(2\right)=0$

Explanation of Solution

Given:

A function is given as

  $f\left(x\right)=\frac{x^2-4}{x^2}$

Calculation:

Put $x=2$ in $f\left(x\right)=\frac{x^2-4}{x^2}$ , we get

  $\begin{array}{c}f\left(2\right)=\frac{2^2-4}{2^2}\\ =0\end{array}$

b.

To determine

To find the value of $f\left(-2\right)$ .

Answer to Problem 7RE

  $f\left(-2\right)=0$

Explanation of Solution

Given information:

A function is given as

  $f\left(x\right)=\frac{x^2-4}{x^2}$

Calculation:

Put $x=-2$ in $f\left(x\right)=\frac{x^2-4}{x^2}$ , we get

  $\begin{array}{c}f\left(-2\right)=\frac{{\left(-2\right)}^2-4}{{\left(-2\right)}^2}\\ =\frac{4-4}{4}\\ =0\end{array}$

c.

To determine

To find the value of $f\left(-x\right)$ .

Answer to Problem 7RE

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

Explanation of Solution

Given information:

A function is given as

  $f\left(x\right)=\frac{x^2-4}{x^2}$

Calculation:

Put $x=-x$ in $f\left(x\right)=\frac{x^2-4}{x^2}$ , we get

  $\begin{array}{l}f\left(-x\right)=\frac{{\left(-x\right)}^2-4}{{\left(-x\right)}^2}\\ =\frac{x^2-4}{x^2}\\ \end{array}$

d.

To determine

To find the value of $-f\left(x\right)$ .

Answer to Problem 7RE

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

Explanation of Solution

Given information:

A function is given as

  $f\left(x\right)=\frac{x^2-4}{x^2}$

Calculation:

Multiply minus sign to both sides

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

e.

To determine

To find the value of $f\left(x-2\right)$ .

Answer to Problem 7RE

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

Explanation of Solution

Given information:

A function is given as

  $f\left(x\right)=\frac{x^2-4}{x^2}$

Calculation:

Put $x=x-2$ in $f\left(x\right)=\frac{x^2-4}{x^2}$ , we get

  $\begin{array}{c}f\left(x-2\right)=\frac{{\left(x-2\right)}^2-4}{{\left(x-2\right)}^2}\\ =\frac{x^2-4x+4-4}{{\left(x-2\right)}^2}\\ =\frac{x^2-4x}{{\left(x-2\right)}^2}\end{array}$

f.

To determine

To find the value of $f\left(2x\right)$ .

Answer to Problem 7RE

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

Explanation of Solution

Given information:

A function is given as

  $f\left(x\right)=\frac{x^2-4}{x^2}$

Calculation:

Put $x=2x$ in $f\left(x\right)=\frac{x^2-4}{x^2}$ , we get

  $\begin{array}{c}f\left(2x\right)=\frac{{\left(2x\right)}^2-4}{{\left(2x\right)}^2}\\ =\frac{4x^2-4}{4x^2}\\ =\frac{4\left(x^2-1\right)}{4x^2}\\ =\frac{x^2-1}{x^2}\end{array}$