Why is fnot a function from R to R if a) f(x) = 1 f(x) is not a function because when x = is undefined is not real √2 0 -1 1 is false is defined has two distinct values f( is true 1/√2
Why is fnot a function from R to R if a) f(x) = 1 f(x) is not a function because when x = is undefined is not real √2 0 -1 1 is false is defined has two distinct values f( is true 1/√2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Why is \( f \) not a function from \( \mathbb{R} \) to \( \mathbb{R} \) if \( f(x) = \frac{1}{x} \)?**
\( f(x) \) is not a function because when \( x = \) [blank], \( f(x) \) [blank] [blank].
**Options:**
- is undefined
- 0
- is false
- is true
- is not real
- -1
- is defined
- \( \frac{1}{\sqrt{2}} \)
- \( \sqrt{2} \)
- 1
- has two distinct values
**Explanation:**
The function \( f(x) = \frac{1}{x} \) is not defined when \( x = 0 \) because division by zero is undefined in mathematics. Therefore, the correct answer is that \( f(x) \) is not a function when \( x = 0 \) because at this point, \( f(x) \) is undefined.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe1bc56e6-20f8-4a3a-902b-39b746310ca0%2F8cb2bdba-60e5-49bc-82e4-330d3e442fb3%2Fw6e7lch_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Why is \( f \) not a function from \( \mathbb{R} \) to \( \mathbb{R} \) if \( f(x) = \frac{1}{x} \)?**
\( f(x) \) is not a function because when \( x = \) [blank], \( f(x) \) [blank] [blank].
**Options:**
- is undefined
- 0
- is false
- is true
- is not real
- -1
- is defined
- \( \frac{1}{\sqrt{2}} \)
- \( \sqrt{2} \)
- 1
- has two distinct values
**Explanation:**
The function \( f(x) = \frac{1}{x} \) is not defined when \( x = 0 \) because division by zero is undefined in mathematics. Therefore, the correct answer is that \( f(x) \) is not a function when \( x = 0 \) because at this point, \( f(x) \) is undefined.
Transcribed Image Text:### Exploring the Function \( f(x) = \sqrt{x} \)
#### Question:
b) Is \( f(x) = \sqrt{x} \) a function?
#### Explanation:
The function \( f(x) = \sqrt{x} \) is described as not a function because when \( x \) is less than 0, \( f(x) \) is undefined.
#### Interactive Elements:
- Options to complete the statement:
- \( x \)
- \(\sqrt{0}\)
- is false
- \( = 0.1 \)
- is defined
- is true
- \( f(x) \)
- \( = 0 \)
- \( < 0 \)
- is undefined
- \( f(0) \)
- \( > 0 \)
#### Conclusion:
For \( f(x) = \sqrt{x} \), \( f(x) \) is undefined for \( x < 0 \), as the square root of a negative number is not defined within the set of real numbers. Hence, we confirm that \( f(x) \) can only be considered a function for \( x \geq 0 \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
