What is Foggy?

Foggy is a term used in mathematics to describe a specific type of composition of functions. When we talk about foggy, we are referring to the composition of two functions, f(x) and g(x), which is written as (f ◦ g)(x). This notation represents the function f(g(x)). In other words, we first apply the function g to the input x, and then apply the function f to the result of g(x).

How to Calculate Foggy

When calculating (f ◦ g)(x), we follow these steps:

1. Start with the input value x.
2. Apply the function g to x, which gives us g(x).
3. Take the result g(x) and apply the function f to it, resulting in f(g(x)).

Example

Let's consider the functions f(x) = 2x + 1 and g(x) = x^2. To calculate (f ◦ g)(x), we follow these steps:

1. Start with the input value x.
2. Apply the function g to x: g(x) = x^2.
3. Take the result g(x) and apply the function f to it: f(g(x)) = 2(x^2) + 1.

Study Guide

When studying foggy, it's important to remember the following key points:

• The order of composition matters: (f ◦ g)(x) is not the same as (g ◦ f)(x).
• Pay attention to the domain and range of the functions f and g to ensure that the composition is well-defined.
• Practice evaluating foggy for different combinations of functions to strengthen your understanding.