Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (g∘g)(-2)

Key Concepts

Function Composition

Function composition involves combining two functions to create a new function. The notation (g∘g)(x) means to apply the function g to itself. This requires first finding g(x) and then substituting that result back into g. Understanding this concept is crucial for evaluating composite functions correctly.

Evaluating Functions

Evaluating a function means substituting a specific input value into the function's formula to find the corresponding output. For example, to evaluate g(-2), you replace x in g(x) with -2. This process is fundamental in finding function values and is necessary for solving problems involving function composition.

Linear Functions

Linear functions are mathematical expressions of the form f(x) = mx + b, where m is the slope and b is the y-intercept. Both ƒ(x) and g(x) in the question are linear functions. Understanding their properties, such as how to graph them and their behavior, is essential for manipulating and composing these functions effectively.