Question

Given (f(x) = |x|), what is the domain of (j(x) = 1/8f(4x+9) - 3)?

a) (D = x ∈ ℝ ,|, x ≥ 0)
b) (D = x ∈ ℝ)
c) (D = x ∈ ℝ ,|, -4 ≤ x ≤ 4)
d) (D = x ∈ ℝ ,|, 0 ≤ x ≤ 9)

Answer 1

The domain of the function j(x) = 1/8f(4x+9) - 3 is x ∈ ℝ.

Step-by-step explanation:

The given function j(x) = 1/8f(4x+9) - 3 is composed of two parts:

1. f(4x+9): This part involves the function f(x) = |x|. It means that whatever value of x we have, we substitute it into 4x+9 and evaluate f at that value. For example, if x = 2, then 4x+9 = 4(2)+9 = 17. So, f(17) = |17| = 17.
2. 1/8f(4x+9) - 3: In this part, we take the value we got from step 1 and multiply it by 1/8. Then, we subtract 3 from that result.

To find the domain of j(x), we need to consider any restrictions on x that arise from f(x). Since f(x) = |x|, it can take any value of x. Therefore, the domain of j(x) is the same as the domain of f(4x+9), which is D = x ∈ ℝ.