Final answer:
To find a function with a domain and range that include all real numbers, option D is the correct answer.
Step-by-step explanation:
To find a function with a domain and range that include all real numbers, we can consider options B, C, and D, since option A has a fractional exponent that restricts the domain and range. Let's analyze each option:
B. f(x) = x¹/4 - 5
Option B has a fractional exponent of 1/4, which means the function's domain and range are not (-∞, +∞).
C. f(x) = x¹/6 - 5
Similarly, option C has a fractional exponent of 1/6, so it also does not have the required domain and range.
D. f(x) = x¹/8 - 5
Option D, on the other hand, has a fractional exponent of 1/8, which means the function's domain and range are indeed (-∞, +∞). Therefore, option D is the correct answer.