a. A function is given by a table of values. Determine whether the function is one-to-one or not. 4 6. 8. 10 g(t) 17 21 15 9. 3. b. Express the given quantity as a single logarithm. In (3a + b) + In (a- 3b)- 2ln (c) c. To convert Fahrenheit to Celsius use f(F) = (F -32) x Find the inverse of the function so you can find the Fahrenheit from knowing the Celsius.
a. A function is given by a table of values. Determine whether the function is one-to-one or not. 4 6. 8. 10 g(t) 17 21 15 9. 3. b. Express the given quantity as a single logarithm. In (3a + b) + In (a- 3b)- 2ln (c) c. To convert Fahrenheit to Celsius use f(F) = (F -32) x Find the inverse of the function so you can find the Fahrenheit from knowing the Celsius.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
A.According to the table, is the function one-to-one or not?
B.Express the given quantity as a single logarithm
C.Convert F to Celcius. Find the inverse of function so you can find the F from knowing the celsius
![## Understanding a Given Function and Its Properties
### a. Determining if a Function is One-to-One
A function is given by a table of values. Determine whether the function is one-to-one or not.
| t | 0 | 2 | 4 | 6 | 8 | 10 |
|-----|-----|-----|-----|-----|-----|----|
| g(t) | 9 | 17 | 21 | 15 | 9 | 3 |
To determine if the function \( g(t) \) is one-to-one, we need to check if each value of \( g(t) \) corresponds to a unique value of \( t \). That is, for \( g(t_1) = g(t_2) \), \( t_1 \) should equal \( t_2 \).
**Analysis**:
- Observing the table, we see that \( g(0) = 9 \) and \( g(8) = 9 \).
- Thus, \( g(t) \) is not one-to-one because the same output (9) is achieved from two different \( t \) values (0 and 8).
### b. Expressing a Quantity as a Single Logarithm
Simplify the given expression into a single logarithm.
\[ \ln (3a + b) + \ln (a - 3b) - 2 \ln (c) \]
**Steps**:
1. Use the logarithm property \( \ln(x) + \ln(y) = \ln(xy) \):
\[ \ln[(3a + b)(a - 3b)] \]
2. Use the logarithm property \( k \ln(x) = \ln(x^k) \):
\[ \ln(c^2) = 2 \ln(c) \]
3. Combine terms:
\[ \ln \left( \frac{(3a + b)(a - 3b)}{c^2} \right) \]
**Result**:
\[ \ln \left( \frac{(3a + b)(a - 3b)}{c^2} \right) \]
### c. Finding the Inverse of the Temperature Conversion Function
#### Convert Fahrenheit to Celsius
To](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d7d2d74-d827-467b-8d8e-9fee9720e388%2F9624e151-cea3-4cf2-83e4-8d3655baee28%2Fesaxiqh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Understanding a Given Function and Its Properties
### a. Determining if a Function is One-to-One
A function is given by a table of values. Determine whether the function is one-to-one or not.
| t | 0 | 2 | 4 | 6 | 8 | 10 |
|-----|-----|-----|-----|-----|-----|----|
| g(t) | 9 | 17 | 21 | 15 | 9 | 3 |
To determine if the function \( g(t) \) is one-to-one, we need to check if each value of \( g(t) \) corresponds to a unique value of \( t \). That is, for \( g(t_1) = g(t_2) \), \( t_1 \) should equal \( t_2 \).
**Analysis**:
- Observing the table, we see that \( g(0) = 9 \) and \( g(8) = 9 \).
- Thus, \( g(t) \) is not one-to-one because the same output (9) is achieved from two different \( t \) values (0 and 8).
### b. Expressing a Quantity as a Single Logarithm
Simplify the given expression into a single logarithm.
\[ \ln (3a + b) + \ln (a - 3b) - 2 \ln (c) \]
**Steps**:
1. Use the logarithm property \( \ln(x) + \ln(y) = \ln(xy) \):
\[ \ln[(3a + b)(a - 3b)] \]
2. Use the logarithm property \( k \ln(x) = \ln(x^k) \):
\[ \ln(c^2) = 2 \ln(c) \]
3. Combine terms:
\[ \ln \left( \frac{(3a + b)(a - 3b)}{c^2} \right) \]
**Result**:
\[ \ln \left( \frac{(3a + b)(a - 3b)}{c^2} \right) \]
### c. Finding the Inverse of the Temperature Conversion Function
#### Convert Fahrenheit to Celsius
To
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning