Real World Function Inverses

What operation of function shall we use to determine if two functions are inverses of each other?

• multiplication

• division

• composition

• addition

A local credit union offers a special account that earns 2.5% annual interest compounded monthly. The tables below show f(x), the account balance in dollars after x months and g(x), the number of months it will take to have an account balance of x dollars. Which statement best describes the relationship between f(x) and g(x)?

• The functions f(x) and g(x) are inverses because the domain of f(x) is the range of g(x) and the range of f(x) is the domain of g(x).

• The functions f(x) and g(x) are not inverses because the x-values and the function values for each function are not the same.

• The functions f(x) and g(x) are inverses because the independent starting value for both functions is the initial deposit of $500.

• The functions f(x) and g(x) are not inverses because the domain of f(x) is not equivalent to the domain of g(x) and the range of f(x) is not equivalent to the range of g(x).

Which statement about the attributes of f(x) and g(x) is NOT true?

• For the situation, the domain of g(x) is the same as the range of f(x).

• For the situation, both functions have the same x-intercept and y-intercept.

• For the situation, both functions have a minimum value of 0.

• For the situation, f(x) and g(x) have the same maximum value.

The graph shows the functions f(x) and g(x) when x is greater than or equal to 0. Which statement about the relationship between f(x) and g(x) is true?

• The functions f(x) and g(x) are inverses of each other because both functions have a restricted domain of [0, ∞).

• The functions f(x) and g(x) are inverses of each other because each function is a reflection of the other function across the line y = x.

• The functions f(x) and g(x) are not inverses of each other.

Is the inverse function found correctly?

• yes

• no

An ​ (a)   takes a previously found result ( a y value) and returns it to its original value (x value). This means you are ​ (b)   a function

• function

• inverse

• 2 or more

• undoing

The inverse has been reflected over which line?

• y = x

• y =1

• y = 0

• y = x + 1

The inverse has been reflected over which line?

• y = x

• y =1

• y = 0

• y = x + 1

Internationally, countries use different systems to measure temperature. In the United States (US), the Fahrenheit system is used. In the US, it is common to represent the conversion function c(f) on a graph. In the European Union (EU), the Celsius system is used. It is common in the EU to represent the conversion function f(c) as a table. Which statement best represents the relationship between the two functions?

• The table and the graph do not represent inverse functions because they are both linear functions.

• The table and the graph represent inverse functions because the independent and dependent values are interchanged for corresponding points on the table and graph.

• The table and the graph do not represent inverse functions because the key attributes of both representations are not the same.

• The table and the graph represent inverse functions because the list of coordinate values for both representations are the same.

Mechanical engineers took measurements to test the design of a new car. The Velocity test measures braking distance at a given velocity. The Braking Distance test measures the maximum velocity to stop in a given distance. The results of the independent tests are shown in the tables. Which statement best represents an accurate conclusion that the engineers can make from the test results?

• The engineers concluded that the results of the braking distance test and the velocity test are inverse functions due to the interchanged domain and range values of each table.

• The engineers concluded that the results of the braking distance test and the velocity test are inverse functions due to both functions having the same x-intercepts and y-intercepts.

• The engineers concluded that the results of the braking distance test and the velocity test are inverse functions due to both functions having a quadratic relationship.

• The engineers did not find any relationship between the two tables.