Question

a(x) = 3x+1 and b(x) = square root of x-4, what is the domain of (b•a)(x)

Answer 1

a(x) = 3x + 1

b(x) = $\sqrt{x- 4}$

(b . a)(x) = $(3x + 1).\sqrt{x - 4}$

(b . a)(x) = $3x\sqrt{x-4} + \sqrt{x - 4}$

We know some things:

There's no square root of a negative number, so,

x - 4 ≥ 0

x ≥ 4

This way, we can say that the domain of (b . a)(x) is:

Dom (b . a)(x) = R ≥ 4

All real numbers higher or equal to 4.