Answers INMT3 Integrated Math 3 Sem 1 26-27Composition of Functions

Comparing a Function and Its Inverse Answers

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The cost table shows the average cost, a(x), of producing x number of earbuds.

(20, 20)

(52, 20)

(20, 52)

(52, 52)

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A function and its inverse are shown on the graph.

f(x) domain: x ≥ 1f–1(x) domain: x ≥ 1

f(x) domain: x ≥ 1f–1(x) range: y ≥ 1

f(x) domain: x ≤ –2f–1(x) domain: x ≤ –2

f(x) domain: x ≤ –2f–1(x) range: y ≤ –2

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

Option

Consider the tables that represent a continuous function and its inverse.

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

The negative reciprocal of the slope of f(x) is the same as the slope of f–1(x).

The y-coordinate of the y-intercept of f(x) is the same as the y-coordinate of the y-intercept of f–1(x).

The opposite of the y-coordinate of the y-intercept of f(x) is the same as the x-coordinate of the x-intercept of f–1(x).

Consider this function.f(x) = |x – 4| + 6If 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?

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

Since the domain of the original function is limited to x 4, the range of the inverse function is y ≤ 1.

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

Since the range of the original function is limited to y 4, the domain of the inverse function is x ≥ 1.

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?

Option

Consider the tables that represent ordered pairs corresponding to a function and its inverse.

According to the tables, f(x) does not have a y-intercept.

According to the tables, f–1(x) does not have an x-intercept.

The domain of f(x) is restricted such that x ≥ 0, so the domain of f–1(x) is restricted such that y ≥ 0.

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 function.What is the y-intercept of f–1(x)?

–16

–12

Option

Table A represents the function that models the stopping distance in feet of a derby car, d(x), based on the velocity in miles per hour of the car, x.Table B represents the function that models the velocity of a car, v(d), in miles per hour based on distance in feet it took the car to stop, d.

Since the functions in both tables are increasing, they are inverses.

Since the functions in both tables are increasing, they are not inverses.

Since for each ordered pair (x, y) for one function there is an ordered pair (y, x) for the other function, the functions are inverses.

Since for each ordered pair (x, y) for one function there is an ordered pair (y, x) for the other function, the functions are not inverses.

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Comparing a Function and Its Inverse Answers

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