# Thread: another relation problem

1. ## another relation problem

It would be great if someone can help me solve this!

2. Hello,
Originally Posted by Kitty216

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))

3. 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.

4. 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