Let ƒ(x) = 3x^2 - 4 and g(x) = x^2 - 3x -4. Find each of the following. (f/g)(-1)

Verified step by step guidance

1. Identify the functions: \( f(x) = 3x^2 - 4 \) and \( g(x) = x^2 - 3x - 4 \).
2. Understand that \((f/g)(x)\) means \(\frac{f(x)}{g(x)}\).
3. Substitute \(x = -1\) into \(f(x)\) to find \(f(-1)\).
4. Substitute \(x = -1\) into \(g(x)\) to find \(g(-1)\).
5. Calculate \((f/g)(-1)\) by dividing \(f(-1)\) by \(g(-1)\).

Key Concepts

Function Notation

Function notation is a way to represent mathematical functions in a clear format. In this case, ƒ(x) and g(x) denote two different functions, where ƒ(x) = 3x² - 4 and g(x) = x² - 3x - 4. Understanding how to evaluate these functions at specific values, such as -1, is crucial for solving the problem.

Division of Functions

The division of functions, denoted as (f/g)(x), involves dividing the output of one function by the output of another. To find (f/g)(-1), you first evaluate ƒ(-1) and g(-1), then divide the results. This concept is essential for understanding how to manipulate and combine functions in algebra.

Evaluating Polynomial Functions

Evaluating polynomial functions involves substituting a specific value into the polynomial expression. For example, to evaluate ƒ(-1) and g(-1), you replace x with -1 in each polynomial. This process is fundamental in algebra, as it allows you to find specific outputs for given inputs, which is necessary for solving the division of functions.