Question

For f(x) =4x+1 g(x)=x²-5, find (f•g)(x)​

Answer 1

Given :

• $\sf f(x) =4x+1$
• $\sf g(x)=x²-5$

To Find :

• $\sf (f . g)(x)$

Solution :

We know that,

$\Large \underline{\boxed{\sf{ (f . g)(x) = f(x) \times g(x) }}}$

By substituting values :

$\sf : \implies (f . g)(x) = (4x+1) \times (x^{2} -5)$

$\sf : \implies (f . g)(x) = 4x(x^{2} -5) +1(x^{2} -5)$

$\sf : \implies (f . g)(x) = 4x^{3} - 20x + x^{2} -5$

$\sf : \implies (f . g)(x) = 4x^{3} + x^{2} - 20x -5$

Hence, answer is :

$\underline{\boxed{\sf{(f . g)(x) = 4x^{3} + x^{2} - 20x - 5}}}$

Answer 2

Answer:

(f · g)(x) = 4x³ + x² - 20x - 5

General Formulas and Concepts:

Pre-Algebra

• Distributive Property

Algebra I

• Combining Like Terms
• Expand by FOIL (First Outside Inside Last)

Step-by-step explanation:

Step 1: Define

f(x) = 4x + 1

g(x) = x² - 5

(f · g)(x) is f(x)g(x)

Step 2: Find (f · g)(x)

1. Substitute:                    (f · g)(x) = (4x + 1)(x² - 5)
2. Expand [FOIL]:             (f · g)(x) = 4x³ - 20x + x² - 5
3. Combine like terms:    (f · g)(x) = 4x³ + x² - 20x - 5