Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the functions given below. SEE FILE ATTATCHED

Answer 1

Answer:

1. $P(x)$ ÷ $Q(x)$---> $\frac{-3x + 2}{3(3x - 1)}$

2. $P(x) + Q(x)$---> $\frac{2(6x - 1)}{(3x - 1)(-3x + 2)}$

3.  $P(x) - Q(x)$---> $\frac{-2(12x - 5)}{(3x - 1)(-3x + 2)}$

4. $P(x)*Q(x)$ --> $\frac{12}{(3x - 1)(-3x + 2)}$

Step-by-step explanation:

Given that:

1. $P(x) = \frac{2}{3x - 1}$

$Q(x) = \frac{6}{-3x + 2}$

Thus,

$P(x)$ ÷ $Q(x)$ = $\frac{2}{3x - 1}$ ÷ $\frac{6}{-3x + 2}$

Flip the 2nd function, Q(x), upside down to change the process to multiplication.

$\frac{2}{3x - 1}*\frac{-3x + 2}{6}$

$\frac{2(-3x + 2)}{6(3x - 1)}$

$= \frac{-3x + 2}{3(3x - 1)}$

2. $P(x) + Q(x)$ = $\frac{2}{3x - 1} + \frac{6}{-3x + 2}$

Make both expressions as a single fraction by finding, the common denominator, divide the common denominator by each denominator, and then multiply by the numerator. You'd have the following below:

$\frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 18x + 4 - 6}{(3x - 1)(-3x + 2)}$

$\frac{12x - 2}{(3x - 1)(-3x + 2)}$

$= \frac{2(6x - 1}{(3x - 1)(-3x + 2)}$

3. $P(x) - Q(x)$ = $\frac{2}{3x - 1} - \frac{6}{-3x + 2}$

$\frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 4 - 18x + 6}{(3x - 1)(-3x + 2)}$

$\frac{-6x - 18x + 4 + 6}{(3x - 1)(-3x + 2)}$

$\frac{-24x + 10}{(3x - 1)(-3x + 2)}$

$= \frac{-2(12x - 5}{(3x - 1)(-3x + 2)}$

4. $P(x)*Q(x) = \frac{2}{3x - 1}* \frac{6}{-3x + 2}$

$P(x)*Q(x) = \frac{2*6}{(3x - 1)(-3x + 2)}$

$P(x)*Q(x) = \frac{12}{(3x - 1)(-3x + 2)}$

Answer 2

Composite functions involve combining multiple functions to form a new function

The functions are given as:

$P(x) = \frac{2}{3x - 1}$

$Q(x) = \frac{6}{-3x + 2}$

$P(x) \div Q(x)$ is calculated as follows:

$P(x) \div Q(x) = \frac{2}{3x - 1} \div \frac{6}{-3x + 2}$

Express as a product

$P(x) \div Q(x) = \frac{2}{3x - 1} \times \frac{-3x + 2}{6}$

Divide 2 by 6

$P(x) \div Q(x) = \frac{1}{3x - 1} \times \frac{-3x + 2}{3}$

Multiply

$P(x) \div Q(x) = \frac{-3x + 2}{3(3x - 1)}$

Hence, the value of $P(x) \div Q(x)$ is $\frac{-3x + 2}{3(3x - 1)}$

P(x) + Q(x) is calculated as follows:

$P(x) + Q(x) = \frac{2}{3x - 1} + \frac{6}{-3x + 2}$

Take LCM

$P(x) + Q(x) = \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)}$

Open brackets

$P(x) + Q(x) = \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}$

Collect like terms

$P(x) + Q(x) = \frac{18x-6x + 4 - 6}{(3x - 1)(-3x + 2)}$

$P(x) + Q(x) = \frac{12x - 2}{(3x - 1)(-3x + 2)}$

Factor out 2

$P(x) + Q(x) = \frac{2(6x -1)}{(3x - 1)(-3x + 2)}$

Hence, the value of P(x) + Q(x) is $\frac{2(6x -1)}{(3x - 1)(-3x + 2)}$

P(x) - Q(x) is calculated as follows:

$P(x) - Q(x) = \frac{2}{3x - 1} - \frac{6}{-3x + 2}$

Take LCM

$P(x) - Q(x) = \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)}$

Open brackets

$P(x) - Q(x) = \frac{-6x + 4 - 18x +6}{(3x - 1)(-3x + 2)}$

Collect like terms

$P(x) - Q(x) = \frac{-18x-6x + 4 + 6}{(3x - 1)(-3x + 2)}$

$P(x) - Q(x) = \frac{-24x +10}{(3x - 1)(-3x + 2)}$

Factor out -2

$P(x) - Q(x) = \frac{-2(12x -5)}{(3x - 1)(-3x + 2)}$

Hence, the value of P(x) - Q(x) is $\frac{-2(12x -5)}{(3x - 1)(-3x + 2)}$

P(x) * Q(x) is calculated as follows:

$P(x) \times Q(x) = \frac{2}{3x - 1} \times \frac{6}{-3x + 2}$

Multiply

$P(x) \times Q(x) = \frac{12}{(3x - 1)(-3x + 2)}$

Hence, the value of P(x) * Q(x) is $\frac{12}{(3x - 1)(-3x + 2)}$

Read more about composite functions at:

https://brainly.com/question/10687170