Question

suppose that the functions \\(s\\) and \\(t\\) are defined for all real numbers \\(x\\) as follows.

\\s(x) = x + 1\\
\\t(x) = 4x + 6\\

find the following.

\\(s \cdot t)(x) = \\
\\(s + t)(x) = \\
\\(s - t)(3) = \\

Explanation:

Find the product function

Using the Function Operations knowledge point

$$ (s \cdot t)(x) = s(x) \cdot t(x) = (x + 1)(4x + 6) = 4x^2 + 6x + 4x + 6 = 4x^2 + 10x + 6 $$

Find the sum function

Using the Function Operations knowledge point

$$ (s + t)(x) = s(x) + t(x) = (x + 1) + (4x + 6) = 5x + 7 $$

Evaluate the difference function

Using the Function Evaluation and Function Operations knowledge points

$$
LATEXBLOCK0
$$

Answer:

Question 1

Suppose that the functions \(s\) and \(t\) are defined for all real numbers \(x\) as follows.

$$
LATEXBLOCK0
$$

Find the following.
\((s \cdot t)(x) =\) <blank>\(4x^2 + 10x + 6\)</blank>

Question 2

\((s + t)(x) =\) <blank>\(5x + 7\)</blank>

Question 3

\((s - t)(3) =\) <blank>\(-14\)</blank>