Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (ƒ∘g)(4)

Key Concepts

Function Composition

Function composition involves combining two functions to create a new function. The notation (ƒ∘g)(x) means to apply g first and then apply f to the result. This is essential for evaluating expressions like (ƒ∘g)(4), where you first find g(4) and then use that output as the input for f.

Evaluating Functions

Evaluating a function means substituting a specific value into the function's formula to find the output. For example, to evaluate g(4) for the function g(x) = -x + 3, you replace x with 4, resulting in g(4) = -4 + 3 = -1. This step is crucial in 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) = 2x - 3 and g(x) = -x + 3 are linear functions, which means their graphs are straight lines. Understanding their properties helps in analyzing their compositions and outputs.