Question

the total surface area of a cylinder with height 5 in. is given by the function \\(g(x) = 2\pi x^2 + 10\pi x\\), where \\(x\\) is the radius, and the function \\(f(x) = 10\pi x\\) gives the surface area of the side of the cylinder. which combined function gives the total surface area of the two bases of the cylinder?

a. \\(f + g\\)
b. \\(f - g\\)
c. \\(g - f\\)
d. \\(f \cdot g\\)

Explanation:

Identify the given functions and their physical meanings

$$
LATEXBLOCK0
$$

Formulate the relationship for the area of the two bases

$$
LATEXBLOCK1
$$

Express the combined function representation

$$ (g - f)(x) = g(x) - f(x) $$

Answer:

• A. \(f + g\)
• B. \(f - g\)
• C. \(g - f\) (Correct answer)
• D. \(f \cdot g\)