Question

If a(x)=3x+1 and b(x)=" alt=" \sqrt{x - 4} " align="absmiddle" class="latex-formula">
what is the domain of (b○a)(x)?​

Answer 1

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}