Composite and Inverse Functions

Vocabulary

composition of functions

operation of combining two functions by using the output of one as the input for the other

domain of a function

set of the first coordinates of the ordered pairs in a function

function

relation in which each element of the domain corresponds to exactly one element of the range

horizontal line test

test that uses horizontal lines to determine whether a function is one-to-one. If any horizontal line intersects the graph in more than one point, the graph is not one-to-one.

identity function

function for which the output is equal to the input

input

value in the domain of a function

inverse function

result of switching the inputs and outputs of a function when the result is also a function. The composition of a function and its inverse is the identity function.

one-to-one function

function in which each output corresponds to exactly one input

output

value in the range of a function

range of a function

set of the second coordinates of the ordered pairs in a function