• Support PF! Buy your school textbooks, materials and every day products Here!

Graph f(x)=ln(arctan(x))

  • Thread starter dekoi
  • Start date
  • #1
dekoi
f(x)=ln(arctan(x))

How does one determine the graph, domain, and range of the above?
 

Answers and Replies

  • #2
789
0
Start with domain, which in turn can help see the range. Look at the outer function...ln(x). For what kind of numbers is this defined? What sort of numbers are not in it's domain? And when you find that out, when does arctan(x) fall into those acceptable ranges?
 
  • #3
dekoi
How does one determine the graph of arctan(x) ?
 
  • #4
789
0
The graph of arctan(x) is something you're going to have to be very familiar. The domain and range of it can be decuded using qualities of inverses. Let's say you have the function f(x), and it's inverse is g(x). Then for any point (a,b) on f(x) there is a corresponding point (b,a) on g(x). Also, the domain and range are opposites. The domain of f(x) is the range of g(x) and the range of f(x) is the domain of f(x). Now we have to restrict the x-values of the arctan(x) graph to maintain functionality. I'll give you a hint, from the tangent graph, pick the section from [itex]-\frac{\pi}{2}[/itex] to [itex]\frac{\pi}{2}[/itex]. Now from that, what's the domain and range of arctan(x)?
 

Related Threads for: Graph f(x)=ln(arctan(x))

  • Last Post
Replies
7
Views
8K
  • Last Post
Replies
3
Views
9K
  • Last Post
Replies
3
Views
1K
Replies
1
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
7
Views
1K
Replies
10
Views
4K
  • Last Post
Replies
5
Views
14K
Top