Answers GA-GSE Pre-CalculusInverse of a Function

Inverse of a Function Answers

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What are the additive and multiplicative inverses of h(x) = x – 24?

additive inverse: j(x) = x + 24; multiplicative inverse: k(x) =

additive inverse: j(x) = ; multiplicative inverse: k(x) = –x + 24

additive inverse: j(x) = –x + 24; multiplicative inverse: k(x) =

additive inverse: j(x) = –x + 24; multiplicative inverse: k(x) = x + 24

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Consider the function h(x) =x2 – 12x + 58.Which represents a domain restriction and the corresponding inverse function?

x ≥ 6; h–1(x) =

x ≥ 12; h–1(x) =

For the constant function v(x) = 1, which statement describes the additive and multiplicative inverses?

Both inverses are equal to v(x).

Neither inverse is equal to v(x).

The additive inverse is equal to v(x), but the multiplicative inverse is not.

The multiplicative inverse is equal to v(x), but the additive inverse is not.

Manish writes the functions g(x) = – 72 and h(x) = –(x + 72)3.Which pair of expressions could Manish use to show that g(x) and h(x) are inverse functions?

and

The table shows several points for function f(x).Which statement correctly identifies a point on the graph of f–1(x)?

The point (4, –7) is on the graph of f(x), so the point (7, –4) will be on the graph of f–1(x).

The point (–2, 15) is on the graph of f(x), so the point (2, –15) will be on the graph of f–1(x).

The point (–4, 19) is on the graph of f(x), so the point (–4, –19) will be on the graph of f–1(x).

The point (10, –14) is on the graph of f(x), so the point (–14, 10) will be on the graph of f–1(x).

For x > 3, values of the function f(x) = –(x – 3)2(x + 2) are negative. On this same interval, which statement correctly describes the values of the additive and multiplicative inverses?

Both the additive inverse and the multiplicative inverse are positive.

Both the additive inverse and the multiplicative inverse are negative.

The additive inverse is positive, while the multiplicative inverse is negative.

The additive inverse is negative, while the multiplicative inverse is positive.

Which statement describes how the graph of a function, h(x), and its inverse, h‒1(x), are related?

The line y = ‒x is the perpendicular bisector of each segment connecting a point on h(x) to the corresponding point on h‒1(x).

The line y = x is the perpendicular bisector of each segment connecting a point on h(x) to the corresponding point on h‒1(x).

The graph of the inverse of h(x) is a reflection over the line y = 0 of the graph of h(x).

The y-axis is the perpendicular bisector of each segment connecting a point on h(x) to the corresponding point on h‒1(x).

Consider the function f(x) = x2 – 331. Chivonne claims a domain restriction x ≥ 0 produces the inverse function f–1(x) = .Which statement describes whether Chivonne is correct?

The expression for f–1(x) is correct, but the domain restriction is not.

The domain restriction is correct, but the expression for f–1(x) is not.

Both the expression for f–1(x) and the domain restriction are correct.

Neither the domain restriction nor the expression for f–1(x) is correct.

Given r(x) = , which represents a domain restriction on r(x) and the corresponding inverse function?

x > 4; r–1(x) =

x > –4; r–1(x) =

Review the graph of function g(x).

(–3, 0)

(0, –3)

(2, 3)

(3, 4)

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

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.

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

(20, 20)

(52, 20)

(20, 52)

(52, 52)

Which answer includes a function, its inverse, and a dashed line that verifies the relationship?

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).

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

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

–16

–12

Option

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.

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.

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

Option

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