Algebra and Trigonometry - Exponential and Logarithmic Functions

These flashcards cover key concepts and definitions from the lecture on Exponential and Logarithmic Functions, focusing specifically on Composite Functions.

Composite Function

A function that is formed when one function is applied to the result of another function, denoted as f(g(x)).

Domain of a Composite Function

The set of all input values x in the domain of g for which f(g(x)) is defined.

Evaluating a Composite Function

The process of finding the value of a composite function for a given input.

Set of All Real Numbers

The domain of a function which includes all values of x from negative infinity to positive infinity.

Exclusion from Domain

Values that cannot be included in the domain of a function due to restrictions such as division by zero.

Distributive Property

A property that states a(b + c) = ab + ac, applied to functions in the context of composite functions.

Equality of Composite Functions

Demonstrating that two composite functions yield the same output for all input values in their domain.

Finding the Domain

The process of determining the values for which a particular function is defined.

Reciprocal Function

A function of the form f(x) = 1/x, which implies that the output is the multiplicative inverse of the input.

Function Decomposition

The process of breaking down a function into two or more simpler functions that, when combined, produce the original function.