Function Composition Quiz

A mathematical expression that represents a relationship between input values (x) and output values (y). It can be visualized as a graph.

A function consisting of an expression under a square root sign. It is used to represent the relationship between the input and output of a function.

A function consisting of an expression under a cube root sign. It is used to represent the relationship between the input and output of a function.

The set of all possible input values (x) for which a function is defined.

The result of performing one function on the output of another function. It can be written as (g∘f)(x).

The function f(x) is applied first, and its output is used as the input for function g(x)

A process where the expression of a function, or a more complex expression, is rewritten in a simpler equivalent form.

The function that represents the relationship between the input value (x) and the output value (y) for the function f(x).

The function that represents the relationship between the input value (x) and the output value (y) for the function g(x).

The initial step in finding the composition (g∘f)(x) is to replace x in g(x) with the entire expression for f(x).

The expression (x-3)/√(x² - 1) represents the function f(x).

The expression 1/∛x represents the function g(x).

Simplify the expression g(f(x)) by combining the expressions for g(x) and f(x) and simplifying the result.

Intermediate algebraic steps are used to simplify the expression (g∘f)(x).

Combining functions to create a new combined function. This new function's output depends both on the input and the results of the previous functions.

Finding the function that represents the composite function (g∘f)(x). This involves substituting and simplifying.

The composite function (g∘f)(x) is defined for all values of x for which f(x) is defined and the output of f(x) is in the domain of g(x).

The result of applying the function f(x) to an input value x.