Let f(x)=x+1‾‾‾‾‾√ and g(x)=3x−5.

Question

Find f∘g and g∘f, and their respective domains.

1. (f∘g)(x)=
2. 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):

Help please, don't understand this! thanks

Answer 1

Did you mean f(x) = √(x+1) ??

I will assume that.

f∘g = f(g(x))
= f(3x-5)
= √((3x-5) - 5)
= √(3x - 10)
domain:
3x-10≥0
3x≥10
x ≥ 10/3
( I will let you switch this to "interval notation, I like the "old way" better)

g∘f = g(f(x))
= g(√(x+1) )
=3√(x+1) - 5

domain: x ≥ -1