Question

Let f(x)=SQRT X+1 and g(x)=3x−5. Find f∘g and g∘f, and their respective domains.

What is the domain of f∘g ?
Answer (in interval notation):

3. (g∘f)(x)=

4. What is the domain of g∘f ?
Answer (in interval notation):

Answer 1

you know that √u has domain u>=0

f(g) = √(g+1) = √(3x-4)
so, its domain is 3x-4 >= 0

g(f) = 3f-5 = 3√(x+1)-5
same domain as f, naturally: x+1 >= 0