Chapter 11.4, Problem 46PPE

To determine

Perform the $f\left(x\right)\cdot g\left(x\right)$ operation

Answer to Problem 46PPE

  $\frac{8x}{x}$

Explanation of Solution

Given:

For $f\left(x\right)=8x,g\left(x\right)=\frac{1}{x},\text{and}h\left(x\right)=\frac{4}{x-5}$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to perform the operation on given expression, first we put the values of $f\left(x\right)=8x,g\left(x\right)=\frac{1}{x},\text{and}h\left(x\right)=\frac{4}{x-5}$ as shown below,

  $\begin{array}{c}f\left(x\right)\cdot g\left(x\right)=8x\cdot \frac{1}{x}\\ =\frac{8x}{x}\end{array}$

Thus, the solution is $\frac{8x}{x}$.