Question

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

\\s(x) = x - 2\\
\\t(x) = 4x + 2\\

find the following.

\\(s \cdot t)(x) = \\
\\(s - t)(x) = \\
\\(s + t)(4) = \\

Explanation:

Define the function multiplication \((s \cdot t)(x)\)

Using the Distributive Property knowledge point

$$
LATEXBLOCK0
$$

Define the function subtraction \((s - t)(x)\)

We subtract the function \(t(x)\) from \(s(x)\) by combining like terms:

$$
LATEXBLOCK1
$$

Evaluate the function addition at a point \((s + t)(4)\)

We first find the sum function \((s + t)(x)\) and then evaluate it at \(x = 4\):

$$
LATEXBLOCK2
$$

Answer:

Question 1

\((s \cdot t)(x) = 4x^2 - 6x - 4\)

Question 2

\((s - t)(x) = -3x - 4\)

Question 3

\((s + t)(4) = 20\)