Question

If a(x)=3x+1 and b(x)=√x-4, what is the domain of (b*a)(x)?

1. (-∞,∞)
2. [0,∞)
3. [1, ∞)
4. [4,∞)

P.S. - the square root is over the (x-4).. not just the x

Answer 1

The domain of (b*a)(x) is x ≥ 4.

Step-by-step explanation:

The domain of a function is the set of all possible x-values for which the function is defined. To find the domain of (b*a)(x), we need to consider the domains of both functions, b(x) and a(x), and determine the overlap. The domain of a(x) is (-∞, ∞) since there are no restrictions on the x-values. The domain of b(x) is x ≥ 4 since the square root function is only defined for non-negative values. Therefore, when we compose b(x) and a(x), the domain of (b*a)(x) is x ≥ 4.

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