Here are the essential concepts you must grasp in order to answer the question correctly.
Function Composition
Function composition involves combining two functions, where the output of one function becomes the input of another. In this case, fg means f(g(x)), which requires substituting g(x) into f(x). Understanding how to perform this substitution is crucial for finding the composite function.
Recommended video:
Domain of a Function
The domain of a function is the set of all possible input values (x-values) for which the function is defined. For rational functions like f(x) and g(x), the domain is restricted by values that make the denominator zero. Identifying these restrictions is essential for determining the valid inputs for the composite function.
Recommended video:
Domain Restrictions of Composed Functions
Rational Functions
Rational functions are ratios of polynomials, expressed in the form f(x) = P(x)/Q(x), where P and Q are polynomials. The behavior of these functions, including their asymptotes and discontinuities, is influenced by the zeros of the denominator. Understanding these characteristics is important for analyzing the functions f(x) and g(x) in the given problem.
Recommended video:
Intro to Rational Functions