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Math Problem Solving: Inverse Functions and Graphing - Prof. Julienne D. Houck, Assignments of Pre-Calculus

Western Michigan University (WMU)Pre-Calculus
Prof. Julienne D. Houck

Homework problems related to functions, inverse functions, and graphing. Students are required to fill tables, plot points, and find inverse functions for given functions. The document also includes problems on linear functions, quadratic functions, and piece-wise defined functions.

Typology: Assignments

Pre 2010

Uploaded on 07/28/2009

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HW 03
Name
Math 1180
Chapter 2: 2.4 - 2.6
1a. Given the function f(x) = −2
5x+ 1, fill in the table below and then plot those points on
the given axes with y=f(x). (They should be colinear—that is, in a line.)
x f(x)
-5
0
2.5
5
-
x
6
y
b. Explain/show why the function fof part ais invertible.
c. Find the inverse function f−1(x). (Remember that usually f−1(x)6=1
f(x).)
d. Using your answer to part c, fill in the given table and plot the points on the axes.
x f−1(x)
-1
0
1
3
-
x
6
y
1
pf3
pf4

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Download Math Problem Solving: Inverse Functions and Graphing - Prof. Julienne D. Houck and more Assignments Pre-Calculus in PDF only on Docsity!

HW 03

Name Math 1180 Chapter 2: 2.4 - 2.

1a. Given the function f (x) = − 25 x + 1, fill in the table below and then plot those points on the given axes with y = f (x). (They should be colinear—that is, in a line.)

x f (x)

x

y 6

b. Explain/show why the function f of part a is invertible.

c. Find the inverse function f −^1 (x). (Remember that usually f −^1 (x) 6 = f (^1 x) .)

d. Using your answer to part c, fill in the given table and plot the points on the axes.

x f −^1 (x)

x

y 6

  1. For each of the following functions, (i) state whether the function is invertible, then (ii) either find the inverse or explain why the function is not invertible.

a. g(x) = 7x^3 − 4 i.

ii.

b. h(x) =

3 x + 6 on domain [− 2 , ∞) i.

ii.

c. k(x) = 7x^4 + 13 i.

ii.

d. ϕ(x) = 12x^2 + 9 on domain [0, ∞) i.

ii.

e. f (x) = −3(2x − 3) − 7 i.

ii.

  1. Suppose f 1 (x) = 4x − 1, f 2 (x) = − 2 x + 8, f 3 (x) = − 12 x + 4, and f 4 (x) = 14 x + 1.

a. Calculate f 2 ◦ f 3 (x)

b. Calculate f 3 ◦ f 2 (x)

c. Calculate f 4 ◦ f 1 (x)

d. What two things can we conclude from parts a, b, and c?

  1. For an object traveling a set course, we know that the time to complete the journey, t, is inversely proportional to the average speed, v. Given this and the knowledge that the trip will take t = 1 hour, 20 minutes at an average speed of v = 43 miles per hour, how long will the trip take at an average speed of v = 31 miles per hour?

8a. Suppose we know that F varies jointly with m 1 and m 2 and inversely with the square of d. Then given F = 636 when m 1 = 5. 98 × 1015 , m 2 = 65, and d = 6378, find the constant of proportionality.

b. Given your answer to part a, find F when m 1 = 77, m 2 = 63, and d = 0.1. (If you did not get an answer to part a, use the constant k = 3. 02 × 10 −^13 .)