domain/range help

• February 12th 2010, 11:30 AM
snypeshow
domain/range help
Hey guys!

I have 2 equations:
f(x) = sin x
g(x) = x^2 - x + 1

The question asks to find fg(x) and f/g(x) (and domain/range for each)

for fg(x) i got:
fg(x) = sin x^3 - sin x^2 + sin x

how would i find the domain and range for this?

and for f/g(x) i got:
f/g(x) = (sin x) / (x^2 - x + 1)

I don't think that can be reduced anymore, but correct me if i'm wrong. And I need help finding the domain and range for this equation too.
• February 12th 2010, 02:55 PM
TKHunny
Domain and Range normally are easier to determine by assuming ALL REAL NUMBERS and only then looking around for things that really are not included.

f(x) = sin(x)

All Real Numbers.
Nothing to throw out.
Done.

g(x) = 1/sin(x)

All Real Numbers
Wait, sin(x) can be zero. We had better avoid $x = k\pi$ where k is an integer.
Done.

Okay, now you do one.
• February 12th 2010, 08:37 PM
snypeshow
thanks! I never thought of it like that!