Thread: 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.

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 where k is an integer.
Done.

Okay, now you do one.

thanks! I never thought of it like that!