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I have accessed your image. The exercise at the bottom of the page asks to find \( (fg)(x) \) for two functions \( f \) and \( g \). Let me solve them for you.

1. **\( f(x) = 2x \) and \( g(x) = 5x + 3 \)**

To find \( (fg)(x) \), we multiply \( f(x) \) and \( g(x) \):

\[
(fg)(x) = f(x) \cdot g(x) = 2x \cdot (5x + 3)
\]
\[
(fg)(x) = 2x(5x) + 2x(3) = 10x^2 + 6x
\]

So, \( (fg)(x) = 10x^2 + 6x \).

2. **\( f(x) = 2x - 1 \) and \( g(x) = 3x - 4 \)**

Similarly, multiply \( f(x) \) and \( g(x) \):

\[
(fg)(x) = (2x - 1) \cdot (3x - 4)
\]
Use distributive property (FOIL method):

\[
(fg)(x) = 2x(3x) + 2x(-4) + (-1)(3x) + (-1)(-4)
\]
\[
(fg)(x) = 6x^2 - 8x - 3x + 4 = 6x^2 - 11x + 4
\]

So, \( (fg)(x) = 6x^2 - 11x + 4 \).

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Would you like more detailed steps or have any questions?

### Related Questions:
1. How would you approach multiplying two functions with more complex terms?
2. What is the general formula for the product of two functions \( f(x) \) and \( g(x) \)?
3. How does the distributive property apply when multiplying polynomials?
4. Can you use the same method to find the product of three functions? If so, how?
5. How does function composition differ from function multiplication?

**Tip:** Always simplify your expressions after multiplying functions to make further analysis easier.

Discover how to multiply polynomial functions with step-by-step solutions. Learn the process of multiplying functions such as f(x) = 2x with g(x) = 5x + 3 and f(x) = 2x - 1 with g(x) = 3x - 4, including detailed examples. Suitable for high school students studying algebra.

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