Let f(x)=x^2+2 and g(x)=(sqrt) 1-x^2. Are f*g, g*f defined?

[bryanx47]

Find the domain and range of f*g. Let f(x)=x^2+2 and g(x)= (sqroot) 1-x^2

Are the functions of f*g and g*f defined? Explain

I have some of this done but want to know if i'm on the right track. Help would be very much appreciated

 

[royhaas]

Re: composite functions

Show what you have done and someone can tell if you are on the right track.

 

[stapel]

I have some of this done but want to know if i'm on the right track.

Um... It's kind of slightly impossible for us to know if you're "on the right track" when we have no idea what you'd tried. :shock:

Please reply with a clear listing of everything you have tried so far, including the exact wording of the exercise and a definition of the "star" operator you are using. Thank you!

Eliz.

P.S. The "star" operator usually means multiplication, so "f*g" would mean (f(x))(g(x)), rather than, say, f(g(x)).

 

[bryanx47]

okay.. up to now i have

f(g(x))
=(sqroot 1-x^2)^2+2
=1-x^2+2
=-x^2+3
which leaves me with no idea with what the domain is, since the randicand is gone..