If:

Question

f(x)= radical x
g(x)= x^2+1

What is the domain of f o g?

I don't really understand how to answer this question.

Answer 1

f{g(x)} = sqrt(x^2+1)

The domain is all numbers greater than 1, unless you also allow the negative square root as one of two radical x values. In that case you can also have
f{g(x)} numbers less than -1.

Answer 2

The formula for f{g(x)} is correct, but I got the domain and range mixed up.

x can have any real value, so the domain of f{g(x)} extends from -infinity to infinity.