Precalculus Exploration 3: Functions and Their Inverse Functions

(Export results to html for the students to view later.) Visual exploration of the graphs of functions and their inverses, in which each student volunteers to explain to the class how to obtain the inverse of the given function and the graph of both the function and its inverse. As we scroll through the document with the class, only the plot and the specification of function f(x) are displayed initially. Each volunteer student must find the inverse function and then describe why the graphs of each are correct.

Problem 5, p. 149.

[Maple Plot]

f(x) = 4*x-3

f^` -1`*`( x)` = 1/4*x+3/4

Problem 6, p. 149.

[Maple Plot]

f(x) = 1/2*x-4

f^` -1`*`( x)` = 2*x+8

Problem 11, p. 150.

[Maple Plot]

f(x) = 3*x-5

f^` -1`*`( x)` = 1/3*x+5/3

Problem 13, p. 150.

[Maple Plot]

f(x) = x^4, 0 <= x

f^` -1`*`( x)` = x^(1/4), 0 <= x

Problem 14, p. 150.

[Maple Plot]

f(x) = 1/x, x <> 0

f^` -1`*`( x)` = 1/x, x <> 0

Problem 16, p. 150.

[Maple Plot]

f(x) = (5-x)^(1/2), x <= 5

f^` -1`*`( x)` = 5-x^2, 0 <= x

Problem 17, p. 150.

[Maple Plot]

f(x) = (4-x^2)^(1/2)

f^` -1`*`( x) does not exist.`

Problem 19, p. 150.

[Maple Plot]

f(x) = (1+x^3)^(1/3)

f^` -1`*`( x)` = (x^3-1)^(1/3)

Problem 21, p. 150.

[Maple Plot]

f(x) = 9-x^2, x <= 0

f^` -1`*`( x)` = -(9-x)^(1/2), x <= 9

Problem 23, p. 150.

[Maple Plot]

f(x) = (x-4)^2-1, 4 <= x

f^` -1`*`( x)` = 4+(x+1)^(1/2), -1 <= x

Problem 24, p. 150.

[Maple Plot]

f(x) = (1-x^3)^(1/3)

f^` -1`*`( x)` = (1-x^3)^(1/3)

Problem 25, p. 150.

[Maple Plot]

f(x) = x/(x-1), x <> 1

f^` -1`*`( x)` = x/(x-1), x <> 1

Problem 26, p. 150.

[Maple Plot]

f(x) = (1-x^2)^(1/2), `&and`(0 <= x,x <= 1)

f^` -1`*`( x)` = (1-x^2)^(1/2), `&and`(0 <= x,x <= 1)