Comparing a Function and Its Inverse

A linear function and its inverse are given. Which tables could be used to verify that the functions are inverses of each other? Select two options.

2 and 4

Consider the tables created with Fahrenheit and Celsius temperatures. Table A represents the function that models Celsius temperature, C(F), based on the given Fahrenheit temperature, F. Which table could be used with Table A to verify that the function modeling Fahrenheit temperature, F(C), based on a given Celsius temperature, C, is the inverse of C(F)?

A

Students are asked to graph the inverse, f-1(x) of an absolute value function, f(x) after restricting its domain. The directions also ask that the graph include a dashed line that can be used to verify that the functions are inverses of each other. Which student's work is correct?

B

A function and its inverse are shown on the graph. Which answer pairs a possible domain restriction for f(x) and its corresponding impact on f-1(x)?

B f(x) domain: x ≥ 1f-1(x) range: y ≥ 1

A function and its inverse are shown on the graph. Which statement describes the relationship between the function and its inverse?

NOT B The domain of both f(x) and f-1(x) is all real numbers.

Which tables could be used to verify that the functions they represent are inverses of each other? Select two options.

Not 2 and 5

Consider this function. f(x) = |x - 4| + 6 If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?

C Since the range of the original function is limited to y 6, the domain of the inverse function is x ≥ 6.

The graph below shows two linear functions. Which explanation could be used to verify whether the functions are inverses?

D The point of intersection of the two functions is not on the line y = x; therefore, the functions are not inverses of each other.

Consider the tables that represent ordered pairs corresponding to a function and its inverse. When comparing the functions using the values in the table, which conclusion can be made?

D The range of f(x) includes values such that y ≥ 1, so the domain of f-1(x) includes values such that x ≥ 1.

Consider the tables that represent a continuous function and its inverse. Which is an accurate comparison of the functions?

A The reciprocal of the slope of f(x) is the same as the slope of f-1(x).