Question

Which is true about the domains and ranges of the functions (f(x) = frac1/8 √x) and (g(x) = 8 √x)?

a) The domain of (f(x)) includes all non-negative real numbers, while the domain of (g(x)) includes all real numbers.
b) The domain of both (f(x)) and (g(x)) includes all non-negative real numbers.
c) The range of (f(x)) includes all non-negative real numbers, while the range of (g(x)) includes all real numbers.
d) The range of both (f(x)) and (g(x)) includes all non-negative real numbers.

Answer 1

The domain of both (f(x) = 1/8 √x) and (g(x) = 8 √x) includes all non-negative real numbers, while their range also includes all non-negative real numbers, making option b) the correct answer.

Step-by-step explanation:

The correct answer to the question regarding the functions (f(x) = \frac{1}{8} \sqrt{x}) and (g(x) = 8 \sqrt{x}) is option b): The domain of both f(x) and g(x) includes all non-negative real numbers. This is because the square root function is not defined for negative numbers, hence the domain for both f(x) and g(x) must be [0, ∞), which includes all non-negative real numbers. As for their ranges, since both are square root functions and are multiplied by a positive constant (1/8 or 8), their outputs can never be negative. Therefore, the range of both functions also includes all non-negative real numbers, which makes option d) partially correct, but since the domain is the issue in question, b) is the fully correct choice.