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) * g(x) }}}`

By substituting values :

`\sf : \implies (f . g)(x) = (4x+1) * (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

(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)

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