8. Given f(x) = 3 and g(x) = - 2x + 5 what is (fg)(x) ?

A. 6x + 15

B. - 6x + 15

C. 6x - 15

D. 6x - 8

To solve the problem of finding \((fg)(x)\), we need to determine the product of the two functions \(f(x)\) and \(g(x)\).

Given:
- \(f(x) = 3\)
- \(g(x) = -2x + 5\)

The product of these two functions is:

\[
(fg)(x) = f(x) \times g(x)
\]

Substituting the given functions:

\[
(fg)(x) = 3 \times (-2x + 5)
\]

Now, distribute the 3:

\[
(fg)(x) = 3 \times -2x + 3 \times 5 = -6x + 15
\]

Thus, the correct answer is:

\[
\boxed{B. -6x + 15}
\]

Would you like details or have any questions?

Here are 5 relative questions:
1. What is the general process for multiplying two functions?
2. How does the distributive property apply to function multiplication?
3. If \(f(x) = x + 2\) and \(g(x) = x - 3\), what is \((fg)(x)\)?
4. How would \((fg)(x)\) change if \(f(x)\) were a variable expression instead of a constant?
5. What happens to the product of functions if one function is zero?

**Tip:** Always double-check your distribution when multiplying expressions to avoid simple arithmetic errors.

Learn how to multiply two functions f(x) = 3 and g(x) = -2x + 5 to find (fg)(x). This problem involves function composition and arithmetic operations on functions. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation