Question

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

a) (-[infinity], 0)
b) [0, [infinity])
c) [1, [infinity])
d) [4, [infinity])

Answer 1

The domain of (b°a)(x) is [4, ∞), option d is correct answer.

Step-by-step explanation:

The domain of (b°a)(x) can be found by considering the restrictions on the composition of functions. The composition of two functions a(x) and b(x), denoted as (b°a)(x), is defined as b(a(x)). In this case, b(x) = √(x-4) and a(x) = 3x + 1.

For (b°a)(x) to be defined, we need the domain of a(x) to be contained within the domain of b(x). The function b(x) involves taking the square root of x-4, so x-4 must be greater than or equal to 0. Solving this inequality, we find that x must be greater than or equal to 4.

Therefore, the domain of (b°a)(x) is [4, ∞). Option d) [4, ∞) is the correct answer.