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) =
`√(x- 4)`

(b . a)(x) =
`(3x + 1).√(x - 4)`

(b . a)(x) =
`3x√(x-4) + √(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.