Question

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

\\f(x) = 2x + 5\\
\\g(x) = 3x\\

find the following.

\\((f \cdot g)(x) = \\)
\\((f + g)(x) = \\)
\\((f - g)(4) = \\)

Explanation:

Find the product function \((f \cdot g)(x)\)

$$
LATEXBLOCK0
$$

Find the sum function \((f + g)(x)\)

$$
LATEXBLOCK1
$$

Evaluate the difference function \((f - g)(4)\)

$$
LATEXBLOCK2
$$

Answer:

Question 1

Suppose that the functions \(f\) and \(g\) are defined for all real numbers \(x\) as follows.
\(f(x) = 2x + 5\)
\(g(x) = 3x\)

Find the following.
\((f \cdot g)(x) =\) <blank>\(6x^2 + 15x\)</blank>

Question 2

Suppose that the functions \(f\) and \(g\) are defined for all real numbers \(x\) as follows.
\(f(x) = 2x + 5\)
\(g(x) = 3x\)

Find the following.
\((f + g)(x) =\) <blank>\(5x + 5\)</blank>

Question 3

Suppose that the functions \(f\) and \(g\) are defined for all real numbers \(x\) as follows.
\(f(x) = 2x + 5\)
\(g(x) = 3x\)

Find the following.
\((f - g)(4) =\) <blank>1</blank>