Message Boards Message Boards

0
|
3761 Views
|
1 Reply
|
1 Total Likes
View groups...
Share
Share this post:
GROUPS:

How to find the domain of composition of 2 functions

Posted 10 years ago
All:

How to find the domain of  composition of 2 functions :
f(g(x) where f(x)= radical( x^2 -5x -6) and g(x) = 4x + 5
using Mathematica

Thanks for your help

Regards,
Bzoo
POSTED BY: Bzoo Msoo
Hi, 

First, determine domains of f and g,  the domain of g is R, for f the domain is:
f = Sqrt[#^2 - 5 # - 6] &;
g = 4 # + 5 &;
Solve[f[x] == 0, x]
Plot[f[x], {x, -10, 15}]
wich gives (-inf,-1) and  (6,+inf) .
Then  for h=f(g):
h = ( # // g // f) &;
Solve[h[x] == 0, x]
Plot[h[x], {x, -10, 15}]
with a result  (-inf,-3/2) and (1/4,+inf) .
The overall domain is  (-inf,-3/2) and (6,+inf) .
Plot[{f[x], h[x]}, {x, -10, 15}]
For more complicated functions you may consider using NSolve or FindRoot.

I.M.
POSTED BY: Ivan Morozov
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract