What is the domain of the function?
For the following two (02) items: Consider the function f(x)=1-\sqrt{(x-1)^{2}}.
- A. (1,\infty)
- B. (-\infty,\infty) ✓
- C. (0,\infty)
- D. (-\infty,\infty)\backslash\{1\}
Correct Answer: B. (-\infty,\infty)
Explanation
The expression involves a cube root of a squared real number, (x-1)^{2/3}, which is well-defined and real for all real values of x. Thus, there are no restrictions on x, and the domain is the set of all real numbers, (-\infty, \infty).
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