Find the functions a) f o g, b) g o f, c) f o f, d) g o g, and their domains.

Question

f(x)= square root of x, g(x)= cube root of 1-x

These are my answers, but I am not sure about them and I only figured out one domain... that is the part that really confuses me. Help please!

a) 5th root of 1-x
Domain?

b) The cube root of (1 minus the square root of x)
Domain?

c) Fourth root of x
Domain= [0, infinity]

d) The cube root of (1 minus the cube root of 1 minus x)
Domain?

Answer 1

a. Odd roots of negative numbers can be negative, thus (-32)^1/5 has a root -2. So the domain of x is all real x.
b.same argument
c. you cannot take the even root of a negative number, so you are correct.
d. same a,b