Question

find its domain.
f(x)=x^2-3
g(x)=sqrt(21-7x)
(f o g) (x)=18-7x
domain of (f o g) (x) is?







The domain of is

Answer 1

(f o g) (x)=18-7x looks like it should be all reals, but remember that the domain of (f o g)(x) is only good when f(x) AND g(x) have that domain as well. g(x) is imaginary for x>3, and hence this limits the domain of (f o g) is
\[x \le 3\]

Answer 2

could you please put it in interval notation?

Answer 3

nevermind i got it :) thanks so much

Answer 4

\[(-\infty,3]\]

Answer 5

you are pretty amazing :) could you maybe answer two more questions??? i will post them.

Answer 6

try me whenever, thanks

Answer 7

I'm about to post em