Answer:
g(f(x)) = [tex]\sqrt{f(x)} +2=\sqrt{x+1} +2[/tex]
Domain = [-1,∞)
Step-by-step explanation:
Given f(x) = x+1 and g(x) = √x + 2
g(f(x)) is a composite function.
g(f(x)) = [tex]\sqrt{f(x)} +2=\sqrt{x+1} +2[/tex]
To find the domain of composite function we must get both domains right (the composed function and the first function used).
The domain of f(x) is all the real numbers.
The domain of g(f(x)) is the values of x provide that the square root is greater than or equal zero
So, x+1 ≥ 0
∴ x ≥ -1
So, the domain = [-1,∞)
