Inverse Functions and Relations Apply, algebra homework help

OPEN ENDED Sketch a graph of a function f that satisfies the following conditions:

f does not have an inverse function f(x) > x for all x f(1) > 0Writing in Math Refer to the information on page 411 to explain how inverse functions can be used in measurement conversions. Point out why it might be helpful to know the customary units if you are given metric units. Demonstrate how to convert the speed of light c = 3.0 × 108 meters per second to miles per hour. 7-2
Inverse Functions
and Relations
Main Ideas
. . Find the inverse of a
function or relation
• Determine whether
two functions or
relations are inverses
New Vocabulary
inverse relation
inverse function
identity function
one-to-one
GET READY for the Lesson
Most scientific
formulas involve measurements given in SI
(International System) units. The SI units for speed are meters per
second. However, the United States uses customary measurements
such as miles per hour
To convert x miles per hour to an approximate equivalent in meters
per second, you can evaluate the following
f(x) = x miles 1600 meters
1 hour
1 hour 1 mile 3600 seconds
or f(x) = x
To convert x meters per second to an approximate equivalent in miles
per hour, you can evaluate the following.
2(x) = xmeters 3600 seconds
1 mile
1 second 1 hour 1600 meters
or g(x) = x
Notice that f(x) multiplies a number by 4 and divides it by 9. The
function g(x) does the inverse operation of f(x). It divides a number by
4 and multiplies it by 9. These functions are inverses.
Find Inverses Recall that a relation is a set of ordered pairs. The inverse
relation is the set of ordered pairs obtained by reversing the coordinates
of each ordered pair. The domain of a relation becomes the range of the
inverse, and the range of a relation becomes the domain of the inverse
KEY CONCEPT
Inverse Relations
Words Two relations are inverse relations if and only if whenever one
relation contains the element (a, b), the other relation contains
the element (b, a).
Examples Q ((1, 2), (3, 4). (5,6)) S = {(2, 1), (4,3), (6,5)
Q and S are inverse relations.
EXAMPLE Find an Inverse Relation
GEOMETRY The ordered pairs of the relation (2, 1), (5, 1), (2, -4)}
are the coordinates of the vertices of a right triangle. Find the
inverse of this relation and determine whether the resulting
ordered pairs are also the vertices of a right triangle.
To find the inverse of this relation, reverse the coordinates of the
ordered pairs.
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