Only some of the toolkit functions have an inverse. See
[link] .
For a function to have an inverse, it must be one-to-one (pass the horizontal line test).
A function that is not one-to-one over its entire domain may be one-to-one on part of its domain.
For a tabular function, exchange the input and output rows to obtain the inverse. See
[link] .
The inverse of a function can be determined at specific points on its graph. See
[link] .
To find the inverse of a formula, solve the equation
for
as a function of
Then exchange the labels
and
See
[link] ,
[link] , and
[link] .
The graph of an inverse function is the reflection of the graph of the original function across the line
See
[link] .
Section exercises
Verbal
Describe why the horizontal line test is an effective way to determine whether a function is one-to-one?
Each output of a function must have exactly one output for the function to be one-to-one. If any horizontal line crosses the graph of a function more than once, that means that
-values repeat and the function is not one-to-one. If no horizontal line crosses the graph of the function more than once, then no
-values repeat and the function is one-to-one.
For the following exercises, find a domain on which each function
is one-to-one and non-decreasing. Write the domain in interval notation. Then find the inverse of
restricted to that domain.
the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement
A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.
A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike
Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.
the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon
