In Exercises 59-64, let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. (fog) (0)

Key Concepts

Function Composition

Function composition involves combining two functions to create a new function. If you have two functions, f(x) and g(x), the composition (fog)(x) means you apply g first and then apply f to the result. This is expressed mathematically as f(g(x)). Understanding this concept is crucial for evaluating the composite function at a specific input.

Evaluating Functions

Evaluating a function means substituting a specific value into the function to find its output. For example, to evaluate f(x) at x = 0, you replace x in the function f with 0. This process is essential for finding the value of composite functions, as you need to evaluate the inner function first before applying the outer function.

Linear vs. Quadratic Functions

Linear functions, like f(x) = 2x - 5 and g(x) = 4x - 1, have a constant rate of change and graph as straight lines. In contrast, quadratic functions, such as h(x) = x² + x + 2, have a variable rate of change and graph as parabolas. Recognizing the differences between these types of functions is important when composing them, as their behaviors and outputs will differ significantly.