# another relation problem

• Aug 3rd 2008, 02:54 AM
Kitty216
another relation problem
http://i146.photobucket.com/albums/r.../relation2.jpg
It would be great if someone can help me solve this!
• Aug 3rd 2008, 02:12 PM
Moo
Hello,
Quote:

Originally Posted by Kitty216
http://i146.photobucket.com/albums/r.../relation2.jpg
It would be great if someone can help me solve this!

Simplify g(x) :
- csc(x)=1/sin(x)
- tan(x)=sin(x)/cos(x)

Therefore g(x)=1/cos(x)

fog(x)=f(g(x))=sin(g(x))=sin(1/cos(x))

gof(x)=g(f(x))=1/cos(f(x))=1/cos(sin(x))
• Aug 3rd 2008, 03:02 PM
Kitty216
yay!! I also got those =] Do you know how to find the domain and range of these functions? This is all new to me heh.
• Aug 6th 2008, 03:30 PM
Moo
Quote:

Originally Posted by Kitty216
yay!! I also got those =] Do you know how to find the domain and range of these functions? This is all new to me heh.

Sorry for the delay :)

For the domain, just remember that you can't divide something by 0, so x for which the denominator is = 0 may not be in the domain ! That's nearly all you need here.
In other cases, you may need to know that, for example, you can't have a negative number under a square root.

For the range, you may need this information : -1 <= cos(x) (or sin(x)) <= 1