Answer: Domain: {x | x ≥ 1}
Explanation: First, we must write the equation for (b ° a)(x).
Write b(x).
b(x) = √(x - 4)
Substitute x in b(x) for a(x) to get (b ° a)(x).
(b ° a)(x) = √(3x + 1 - 4)
Simplify the right side of the equation.
(b ° a)(x) = √(3x - 3)
To find the domain, write this function as an inequality greater than or equal to 0.
√(3x - 3) ≥ 0
Raise both sides to the power of 2.
3x - 3 ≥ 0
Add 3 to both sides.
3x ≥ 3
Divide both sides by three.
x ≥ 1
Write this inequality as your domain in set notation.
Domain: {x | x ≥ 1}
