Let fx squareroot x 1 and gx 3x 4 f gx What is the doma

Let f(x) = squareroot x + 1 and g(x) = 3x - 4. (f g)(x) = What is the domain of f g ? Answer (in interval notation): (g f)(x) = What is the domain of g f? Answer (in interval notation): If a domain includes more than one interval, write the intervals separated by the \"union\" symbol, U. entered as \"U\". If needed, enter - infinity as \"-infinity\" and infinity as \"infinity\".

Solution

f(x) = sqrt(x +1) g(x) = 3x -4

1. (f og)(x)

Plug x = g(x) in f(x)

(f og)(x) = sqrt(3x -4 +1) = sqrt(3x -3)

2. Domain of ( f o g)(x)

3x -3>=0

x>= 1

[ 1, infinity)

3. (g o f)(x) plug x= f(x) in g(x)

= 3(sqrt(x +1) -4

Domain : (x +1) >=0

x >= -1

[ - 1, inf)