arithmetic/composition problem

Question

What are the domains (in interval notation) of these two functions:

1. (f of g) (x) = √(3x-4)
2. (g of f) (x) = 3√(x+1) -5

**everything in parenthesis is square rooted (sorry it's unclear)

Answer 1

What are the domains (in interval notation) of these two functions:

set each of the results ≥0 and get:

1. (f of g) (x) = √(3x-4) [4/3, ∞)

2.(g of f) (x) = 3√(x+1) -5 [-1, ∞]

what do you guys think? let me know

Answer 2

So the most important thing to know is you cannot have a negative number under the square root ( you can have 0), so we need to solve for those values to find the domain:

1. 3x-4≥0, 3x≥4, x≥4/3 or x: [4/3,∞)
2. x+1≥0, x≥-1 or x: [-1,∞)