2.5 Inverse Functions Flashcards
requires that every element of the domain corresponds to exactly one element of the range
function
requires that every element of the domain corresponds to exactly one element of the range and that every element of the range corresponds to exactly one element of the domain
one-to-one function
Horizontal Line Test
If a horizontal line is drawn across a relation and does not intersect the graph in more than one location, then the relation is one-to-one if and only if the relation passed the vertical line test as well.
Vertical Line Test
If a vertical line is drawn across a relation and does not intersect the graph in more than one location, then the relation is a function.
The graph of a one-to-one functions never has the same _________ for two different x-coordinates on a graph
y-coordinate
A function that is one-to-one is referred to as an ________.
invertible function
What is the symbol referring to the inverse of
How do you find the inverse of a one-to-one function that is a set of ordered pairs?
Interchange the coordinates of each ordered pair
How could you find an inverse of a function that is not a set of ordered pairs?
1) Reverse a composition
2) Switch and solve method
What is the switch and solve method?
1) Replace f(x) with y.
2) Interchange x and y.
3) Solve for y.
4) Replace y with f(x).
How can you prove graphically that two functions are inverses of one another?
Draw the line y = x.
Graph both functions.
The functions are inverses if they reflect about y = x.
What is the relationship between the domain and range of a function and the domain and range of its inverse?
The domain of the function is the range of the inverse.
The range of the function is the domain of the inverse.
How do you prove algebraically that two functions are inverses.
Compute f ￮ g and g ￮ f. If both answers work out to “x”, then f and g are inverses.
