How to rank random function from smallest to largest with inverse f included?

In summary, the ranking for the given values from smallest to largest is as follows: f−1(0) = 1, f(0) = 3, f(5) = 2, f−1(5) = 4. The confusion regarding f−1(0) is due to a misunderstanding of inverse functions. The correct value for f−1(0) is 4, as f(4) = 0, not f(0) = 4.
  • #1
gurpalc
16
0

Homework Statement



The graph of y=f(x) is shown below.

http://Newton.science.sfu.ca/cgi-bin/plot.png?file=public_public_1346904771_18810161_plot.data
Rank the following from smallest(1) to largest(4).

f−1(0)
f(0)
f(5)
f−1(5)

Homework Equations



none available

The Attempt at a Solution



f−1(0) 1
f(0) 3
f(5) 2
f−1(5) 4


Because if f(0) is 4, wouldn't that make the co-ordinates (0,4) so inverse would be (4, 0) so inverse f(0) would be 0 no? But I know this is wrong. I don't what I am doing wrong.
Please help
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Knowing that f(0)= 4 tells you that [itex]f^{-1}(4)= 0[/itex], not [itex]f ^{-1}(0)[/itex]. What you need is some x such that f(x)= 0. Where is f(x)= 0 on your graph?
 

Related to How to rank random function from smallest to largest with inverse f included?

What is a random function?

A random function is a mathematical function that generates a random output for a given input. It is commonly used in statistics, probability, and computer science.

What does it mean to rank a random function from smallest to largest?

Ranking a random function from smallest to largest means arranging the output values of the function in ascending order. This allows for easier comparison and analysis of the function's behavior.

Why is it important to include inverse f in ranking a random function?

Including inverse f, or the inverse of the random function, is important because it allows for a more complete understanding of the function's behavior. It also ensures that the ranking is accurate and consistent.

What are some methods for ranking a random function from smallest to largest with inverse f included?

One method is to plot the function and its inverse on a graph and visually compare the values. Another method is to create a table of values for both the function and its inverse and compare them. Additionally, mathematical techniques such as calculus and algebra can be used to determine the relative sizes of the function and its inverse.

Are there any limitations or considerations when ranking a random function with inverse f included?

One limitation is that the function and its inverse must be defined for all input values. Also, some random functions may have complex or undefined inverse functions, making ranking difficult. It is also important to consider the domain and range of the function and its inverse when ranking them.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
7
Views
461
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
11
Views
2K
  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
  • Precalculus Mathematics Homework Help
Replies
6
Views
2K
  • Precalculus Mathematics Homework Help
Replies
17
Views
3K
  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
  • Precalculus Mathematics Homework Help
Replies
7
Views
2K
Replies
2
Views
536
  • Engineering and Comp Sci Homework Help
Replies
9
Views
990
Back
Top