How to solve for f_n(x) in Stewart Calculus text's review section?

In summary, the conversation discusses the problem of solving for f_n(x) using the given equations involving f_0(x) and f_{n+1}(x). The conversation also includes attempts at solving the problem and finding the pattern for f_n(x), with the final conclusion that the solution is f_n(x) = x^{2^{n+1}}, which satisfies the given requirements.
  • #1
Jeff Ford
155
2
I'm going through the review section of the Stewart Calculus text and I'm stuck on this problem.

Given
[itex]
f_0(x) = x^2
[/itex]
and
[itex]
f_0(f_n(x)) = f_{n+1}(x) , n = 0,1,2...
[/itex]
how do you solve for
[itex]
f_n(x)
[/itex]
 
Last edited:
Physics news on Phys.org
  • #2
The only place I can think to start is making [itex] (f_n(x))^2 = f_{n+1}(x) [/itex], but that's as far as I got
 
  • #3
Now, f1(x) = f0(f0(x)) = f0(x2) = x4
f2(x) = f0(f1(x)) = f0(x4) = x8
f3(x) = f0(f2(x)) = ...
f4(x) = f0(f3(x)) = ...
So what's fn(x)?
Can you go from here?
Viet Dao,
 
  • #4
From that I get [itex] f_n(x) = x^{2^{n+1}} [/itex] but that doesn't work for [itex] f_0(x) = x^2 [/itex]. That's the same answer the book has, so maybe I wrote the requirements down wrong. I'll have to check when I get home if this had to work for 0.
 
  • #5
Yes it does. Never mind.

Thanks Viet Dao!
 

FAQ: How to solve for f_n(x) in Stewart Calculus text's review section?

1. What does it mean to be "stuck" on a function?

Being "stuck" on a function means that you are unable to make progress or find a solution to a specific function or problem. It could be due to a lack of understanding, incorrect approach, or a complex problem.

2. How do I get "unstuck" on a function?

To get "unstuck" on a function, you could try breaking down the problem into smaller, more manageable parts. You can also seek help from colleagues or consult online resources for different perspectives and approaches.

3. What are some common reasons for getting "stuck" on a function?

Some common reasons for getting "stuck" on a function include not understanding the problem or requirements, using incorrect syntax or logic, or encountering a complex or multi-layered problem.

4. How can I improve my problem-solving skills when dealing with a "stuck" function?

Improving problem-solving skills takes practice and patience. You can start by breaking down problems into smaller parts, seeking help and advice from mentors or colleagues, and practicing regularly with different types of problems.

5. Are there any tools or techniques that can help me when I am "stuck" on a function?

Yes, there are several tools and techniques that can help you when you are "stuck" on a function. These include debugging tools, flowcharts, pseudocode, and brainstorming with others. You can also try taking breaks and approaching the problem with a fresh perspective.

Similar threads

Apparent weight problem (kinematics + conservation of Energy + Newton's laws)
2
Replies
41
Views
2K
I Regarding dominated convergence theorem in Folland
Replies
5
Views
385
How Does Elevator Physics Affect the Work Done by a Cable?
Replies
2
Views
2K
How Do You Calculate Wire Extension Under Sudden Loads?
Replies
15
Views
802
I Uniform closure of algebra of bounded functions is uniformly closed
Replies
2
Views
518
How do write the force diagram for the following situation?
Replies
2
Views
1K
MHB Uniform convergence - Length of graph
Replies
21
Views
2K
A Constructing PDFs for Max Likelihood Density Estimation Problem
Replies
2
Views
2K
B Let f_n denote an element in a sequence of functions that converges
Replies
7
Views
2K
Stretched spring attached to the center of a pure rolling disk
Replies
11
Views
473

Hot Threads

Recent Insights

Back
Top