In Exercises 3744, none of the functions is one-to-one. State at least one way of

In Exercises 1 and 2, write a table that repre- sents the inverse of the function given by the table.

In Exercises 1 and 2, write a table that repre- sents the inverse of the function given by the table.

In Exercises 3 and 4, the graph of a function f is given. Sketch the graph of the inverse function of f and give the coordinates of three points on the inverse.

In Exercises 3 and 4, the graph of a function f is given. Sketch the graph of the inverse function of f and give the coordinates of three points on the inverse.

In Exercises 58, graph f and its inverse in parametric mode (see Example 2).

In Exercises 58, graph f and its inverse in parametric mode (see Example 2).

In Exercises 58, graph f and its inverse in parametric mode (see Example 2).

In Exercises 58, graph f and its inverse in parametric mode (see Example 2).

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).f 1x2 x 1

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).f 1x2 1x5 12 3 f 1x2 5 2x3

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).f 1x2 5 23x 2

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).f 1x2 1 2x

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).f 1x2 x x2 1 f 1x2 1

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).

In Exercises 922, find the rule for the inverse of the given function. Solve your answers for y and, if possible, write in function notation (see Examples 3 and 4).

In Exercises 2330, use a calculator and the Horizon- tal Line Test to determine whether the function f is one-to-one. f 1x2 x4 4x2 3

In Exercises 2330, use a calculator and the Horizon- tal Line Test to determine whether the function f is one-to-one.ff 1x2 x4 4x 3

In Exercises 2330, use a calculator and the Horizon- tal Line Test to determine whether the function f is one-to-one f 1x2 x3 x 5

In Exercises 2330, use a calculator and the Horizon- tal Line Test to determine whether the function f is one-to-one. 2x 6 for x 7 3

In Exercises 2330, use a calculator and the Horizon- tal Line Test to determine whether the function f is one-to-one.x 3 for x 3

In Exercises 2330, use a calculator and the Horizon- tal Line Test to determine whether the function f is one-to-one.f 1x2 e

In Exercises 2330, use a calculator and the Horizon- tal Line Test to determine whether the function f is one-to-one. f 1x2 x5 2x4 x2 4x 5

In Exercises 2330, use a calculator and the Horizon- tal Line Test to determine whether the function f is one-to-one.1x2 x3 4x2 x 10

In Exercises 3136, each given function has an inverse function. Sketch the graph of the inverse function.f 1x2 2x 3

In Exercises 3136, each given function has an inverse function. Sketch the graph of the inverse function.f 1x2 23x 2

In Exercises 3136, each given function has an inverse function. Sketch the graph of the inverse function.f 1x2 0.3x5 2

In Exercises 3136, each given function has an inverse function. Sketch the graph of the inverse function.f 1x2 23 x 3

In Exercises 3136, each given function has an inverse function. Sketch the graph of the inverse function.f 1x2 25 x3 x 2

In Exercises 3136, each given function has an inverse function. Sketch the graph of the inverse function.1x2 e x2 1 for x 0 0.5x 1 for x 7

In Exercises 3744, none of the functions is one-to- one. State at least one way of restricting the domain of the function so that the restricted function has an inverse that is a function. Then find the rule of the inverse function (see Example 6).

In Exercises 3744, none of the functions is one-to- one. State at least one way of restricting the domain of the function so that the restricted function has an inverse that is a function. Then find the rule of the inverse function (see Example 6).

In Exercises 3744, none of the functions is one-to- one. State at least one way of restricting the domain of the function so that the restricted function has an inverse that is a function. Then find the rule of the inverse function (see Example 6).

In Exercises 3744, none of the functions is one-to- one. State at least one way of restricting the domain of the function so that the restricted function has an inverse that is a function. Then find the rule of the inverse function (see Example 6).

In Exercises 3744, none of the functions is one-to- one. State at least one way of restricting the domain of the function so that the restricted function has an inverse that is a function. Then find the rule of the inverse function (see Example 6).

In Exercises 3744, none of the functions is one-to- one. State at least one way of restricting the domain of the function so that the restricted function has an inverse that is a function. Then find the rule of the inverse function (see Example 6).

In Exercises 3744, none of the functions is one-to- one. State at least one way of restricting the domain of the function so that the restricted function has an inverse that is a function. Then find the rule of the inverse function (see Example 6).f 1x2 1 x2 1

In Exercises 3744, none of the functions is one-to- one. State at least one way of restricting the domain of the function so that the restricted function has an inverse that is a function. Then find the rule of the inverse function (see Example 6).f 1x2 31x 52 2 2

In Exercises 4550, use composition to show that f and g are inverses of each other (see Example 7).f 1x2 x 1 g1x2 x 1

In Exercises 4550, use composition to show that f and g are inverses of each other (see Example 7).f 1x2 2x 6 g1x2 x 2 3

In Exercises 4550, use composition to show that f and g are inverses of each other (see Example 7).f 1x2 1 x 1 g1x2 1 x

In Exercises 4550, use composition to show that f and g are inverses of each other (see Example 7).f 1x2 3 2x 5 g1x2 3 5x

In Exercises 4550, use composition to show that f and g are inverses of each other (see Example 7).f 1x2 x5 g1x2 25 x

In Exercises 4550, use composition to show that f and g are inverses of each other (see Example 7).f 1x2 x3 1 g1x2 23 x 1

Show that the inverse function of the function f whose rule is is f 1x2 f itself. 2x 1 isf itself

List three different functions (other than the one in Exercise 51), each of which is its own inverse. Many correct answers are possible.

Critical Thinking Let m and b be constants with Show that the function is one-to-one, and find the rule of the inverse function

Critical Thinking Prove that the function of Example 5c is one-to-one by showing that it satisfies the definition: If then Hint: Use the rule of f to show that when then If this is the case, then it is impossible to have when

Critical Thinking Show that the points and are symmetric with respect to the line as follows: a. Find the slope of the line through P and Q. b. Use slopes to show that the line through P and Q is perpendicular to c. Let R be the point where the line intersects Since R is on it has coordinates (c, c) for some number c, as shown in the figure. Use the distance formula to show that has the same length as Conclude that the line is the perpendicular bisector of Therefore, P and Q are symmetric with respect to the line y x. PQ. y x PR RQ. PQ. y x, y x y x. y x Q 1b, a2 P 1a, b2 f 1a2 f 1b2 a b. f 1a2 f 1b2 a b. a b, f 1a2 f 1b2. h1x2 1 0.2x3 f 1 . m 0. f 1x2 mx b

Let C be the temperature in degrees Celsius. Then the temperature in degrees Fahrenheit is given by Let g be the function that converts degrees Fahrenheit to degrees Celsius. Find the rule of g and show that g is the inverse function of f.

The graph of a function f is shown in the figure. Sketch the graph of the inverse of f

In Exercises 6873, find the inverse relation of each function. If the inverse is a function, write its rule in function notation.

In Exercises 6873, find the inverse relation of each function. If the inverse is a function, write its rule in function notation.

In Exercises 6873, find the inverse relation of each function. If the inverse is a function, write its rule in function notation.

In Exercises 6873, find the inverse relation of each function. If the inverse is a function, write its rule in function notation.f 1x2 2x 1

In Exercises 6873, find the inverse relation of each function. If the inverse is a function, write its rule in function notation.

In Exercises 6873, find the inverse relation of each function. If the inverse is a function, write its rule in function notation.f 1x2 25 x f 1x2 25 x 7 3 1

In Exercises 7476, determine whether or not the given function is one-to-one. Give reasons for your answer. If so, graph the inverse function.

In Exercises 7476, determine whether or not the given function is one-to-one. Give reasons for your answer. If so, graph the inverse function.f 1x2 1 x f 1x2 0.02x3 0.04x2 0.6x 4

In Exercises 7476, determine whether or not the given function is one-to-one. Give reasons for your answer. If so, graph the inverse function.f 1x2 0.2x3 4x2 6x 15

In Exercises 7780, use composition to verify that f and g are inverses.f 1x2 4x 6 g1x2 0.25x 1.5

In Exercises 7780, use composition to verify that f and g are inverses.f 1x2 x3 1 g1x2 23 x 1

In Exercises 7780, use composition to verify that f and g are inverses.f 1x2 2x 1 x 3 g1x2 3x 1

In Exercises 7780, use composition to verify that f and g are inverses.f 1x2 x 1 x 1 g1x2 x 1