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.
if three forces F1.f2 .f3 act at a point on a Cartesian plane in the daigram .....so if the question says write down the x and y components ..... I really don't understand
a fixed gas of a mass is held at standard pressure temperature of 15 degrees Celsius .Calculate the temperature of the gas in Celsius if the pressure is changed to 2×10 to the power 4
