so this is one of those problems I absolutely did not solve after numerous attempts. The relations are already troubling me.. yet they also want me to find the domain and range.. I'm lost =[
For , you simply multiply.
To find the domain, notice that if the denominator equals 0, it makes the function undefined. So , or . So thus far, the domain is and . But also notice the square root in the denominator, so x cannot be negative. So the domain is and .
The range is a bit trickier. I'm not really sure how to get it either.
C and D are compositions of functions. You might want to check here for reference, Composition of Functions
This gets really really messy; I didn't even bother trying to work this out by hand; but according to my TI-89 calculator, the composition should look something like this:
This is obviously very messy to work with. I would suggest using a graphing calculator to approximate the domain and range.