
Concept explainers
(a).
Make tables for f(x) and g(x) using n = 3 and n = 4.
(a).

Explanation of Solution
Given:
Calculation:
n =3 | n=4 | |||
x | ||||
-3 | -27 | -1.442 | 81 | No real solution |
-2 | -8 | -1.260 | 16 | No real solution |
-1 | -1 | -1 | 1 | No real solution |
0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 |
2 | 8 | 1.260 | 16 | 1.189 |
3 | 27 | 1.442 | 81 | 1.316 |
Since the radicand of a radical with even index has to be non-negative.
(b).
Graph the equations.
(b).

Explanation of Solution
Calculation:
From part (a),
n =3 | n=4 | |||
x | ||||
-3 | -27 | -1.442 | 81 | No real solution |
-2 | -8 | -1.260 | 16 | No real solution |
-1 | -1 | -1 | 1 | No real solution |
0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 |
2 | 8 | 1.260 | 16 | 1.189 |
3 | 27 | 1.442 | 81 | 1.316 |
Plot the points on the coordinate plane and graph the equations:
(c).
Find the equations that are functions and the functions that are one-to-one.
(c).

Answer to Problem 58PPS
All are functions and all except
Explanation of Solution
Given:
Calculation:
From part (b) ,
Since the graph of all the equations pass the vertical line test , that is any vertical line intersects the graph at only one point. So, all the equations are functions.
Since the graph of the function
(d).
Find the values of n for which f(x) and g(x) are inverses of each other.
(d).

Answer to Problem 58PPS
Explanation of Solution
Given:
Calculation:
From part (c) ,
Since
A function has an inverse if and only if it is one-to-one.
From the same rule, since
Also , we can observe from the graph :
If two functions are inverse of each other , their graph is symmetric along the line
Since the graphs of the functions
But , the graphs of the functions
(e).
Find the conclusions that you can make about
(e).

Answer to Problem 58PPS
For positive even values of n , the pair of functions are not inverses.
For positive odd values of n, the pair of functions are inverses.
Explanation of Solution
Given:
Calculation:
For positive even values of n , the pair of functions are not one-to −one . Hence are not inverses of each other. Here , the domain of
While for postitive odd values of n , the pair of functions are one-to-one .Hence they are inverses of each other.
Chapter 7 Solutions
Algebra 2
Additional Math Textbook Solutions
Basic Business Statistics, Student Value Edition
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
University Calculus: Early Transcendentals (4th Edition)
A First Course in Probability (10th Edition)
- Answer this questionarrow_forward1. vector projection. Assume, ER1001 and you know the following: ||||=4, 7=-0.5.7. For each of the following, explicitly compute the value. འབ (a) (b) (c) (d) answer. Explicitly compute ||y7||. Explain your answer. Explicitly compute the cosine similarity of and y. Explain your Explicitly compute (x, y). Explain your answer. Find the projection of onto y and the projection of onto .arrow_forward2. Answer the following questions using vectors u and v. --0-0-0 = find the the cosine similarity and the angle between u and v. འརྒྱ (a) (b) find the scalar projection of u onto v. (c) find the projection of u onto v. (d) (e) (f) find the scalar projection of onto u. find the projection of u onto u. find the projection of u onto and the projection of onto . (Hint: find the inner product and verify the orthogonality)arrow_forward
- Using f(x) = log x, what is the x-intercept of g(x) = log (x + 4)? Explain your reasoning. Please type out answerarrow_forwardThe function f(x) = log x is transformed to produce g(x) = log (x) – 3. Identify the type of transformation and describe the change. Please type out answerarrow_forwardEach graph below is the graph of a system of three linear equations in three unknowns of the form Ax = b. Determine whether each system has a solution and, if it does, the number of free variables. A. O free variables ✓ B. no solution C. no solution D. no solution E. 1 free variable F. 1 free variablearrow_forward
- Solve the following systems of equations and show all work.y = x2 + 3y = x + 5 Please type out answerarrow_forwardSolve the following system of equations. Show all work and solutions.y = 2x2 + 6x + 1y = −4x2 + 1 Please type out answerarrow_forwardDalia buys 20 collectible gems per month. Grace sells 10 gems from her collection of 120 each month. When will Dalia have more gems than Grace? Show your work. Dear Student If You Face any issue let me know i will solve your all doubt. I will provide solution again in more detail systematic and organized way. I would also like my last 3 questions credited to mearrow_forward
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education





