SOLUTION: Please, someone help me with these exercises. I highly appreciate. 1- Determine whether the equation defines Y as a function of X. X^2 + (Y-1)^2=4 2- Find the functions fo

Algebra ->  Systems-of-equations -> SOLUTION: Please, someone help me with these exercises. I highly appreciate. 1- Determine whether the equation defines Y as a function of X. X^2 + (Y-1)^2=4 2- Find the functions fo      Log On


   

Question 946577: Please, someone help me with these exercises. I highly appreciate.
1- Determine whether the equation defines Y as a function of X.
X^2 + (Y-1)^2=4
2- Find the functions fog, gof, fof and gog and their domains.
F(x)= x^3+2, g(x)= ^3radical x

Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
(1)
No. That is a circle.

(2)
Maybe you want g%28x%29=root%283%2Cx%29 ?

Form the indicated compositions, and then decide or examine. Easier on paper than using typed text.

g%28g%28x%29%29=root%283%2C%28root%283%2Cx%29%29%29 and exponents for the notation may be easier to manage.
g%28g%28x%29%29=%28x%5E%281%2F3%29%29%5E%281%2F3%29
g%28g%28x%29%29=x%5E%28%281%2F3%29%281%2F3%29%29
g%28g%28x%29%29=x%5E%281%2F9%29
highlight%28g%28g%28x%29%29=root%289%2Cx%29%29. The domain AND range for this is all real numbers. No restrictions.