Question

If a(x) = 3x + 1 and b (x) = StartRoot x minus 4 EndRoot, what is the domain of (b circle a) (x)?

Answer 1

Answer:

  x ≥ 1

Step-by-step explanation:

There are no domain restrictions on a(x), so we can find the domain of the composite function by looking at that composition:

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

The argument of the square root function must be non-negative, so we must have ...

  3(x -1) ≥ 0

  x -1 ≥ 0 . . . . . divide by 3

  x ≥ 1 . . . . . . . add 1

The domain of b(a(x)) is x ≥ 1.