What is (fg)(x)?
f(x)=3x+5
g(x)=x2–4x–5

The expression \((fg)(x)\) represents the product of the two functions \(f(x)\) and \(g(x)\). It is calculated by multiplying \(f(x)\) by \(g(x)\).

Given:
- \(f(x) = 3x + 5\)
- \(g(x) = x^2 - 4x - 5\)

The product of these functions is:

\[
(fg)(x) = f(x) \cdot g(x) = (3x + 5)(x^2 - 4x - 5)
\]

Now let's expand this expression:

\[
(fg)(x) = 3x(x^2 - 4x - 5) + 5(x^2 - 4x - 5)
\]
\[
= 3x^3 - 12x^2 - 15x + 5x^2 - 20x - 25
\]
\[
= 3x^3 - 7x^2 - 35x - 25
\]

Thus, \((fg)(x) = 3x^3 - 7x^2 - 35x - 25\).

Would you like further details or explanations?

Here are 5 related questions:
1. How do you find the composition of functions \((f \circ g)(x)\)?
2. How can you factor the polynomial \(g(x) = x^2 - 4x - 5\)?
3. What is the derivative of \((fg)(x)\)?
4. How do you find the inverse of a function?
5. Can you express \((fg)(x)\) as a factored form?

**Tip:** Always distribute each term carefully when multiplying polynomials to avoid common errors.

What is (fg)(x)? f(x)=3x+5 g(x)=x^2–4x–5

Learn how to multiply the functions f(x) = 3x + 5 and g(x) = x^2 - 4x - 5 to find (fg)(x). This detailed step-by-step solution covers algebraic multiplication of polynomials and the application of the distributive property. Suitable for students in Grades 9-12.

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