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Which of the following is an example of a function with a domain (-[infinity],+[infinity]) and a range (-[infinity],+[infinity])?

A. f(x) = x¹/3 - 5
B. f(x) = x¹/4 - 5
C. f(x) = x¹/6 - 5
D. f(x) = x¹/8 - 5

User Cessor
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1 Answer

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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.

User Nathan Ratcliff
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