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.
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits