Q231 / 270 · NDA 2025 (Phase 2) · Mathematics
For the following two (02) items:
Consider the function $f(x) = 1 - \sqrt[3]{(x-1)^2}$.
What is the domain of the function?
Consider the function $f(x) = 1 - \sqrt[3]{(x-1)^2}$.
What is the domain of the function?
- A$(1, \infty)$
- Correct answerB$(-\infty, \infty)$
- C$(0, \infty)$
- D$(-\infty, \infty) \setminus \{1\}$
Solution
The given function is $f(x) = 1 - \sqrt[3]{(x-1)^2}$.
The expression inside the cube root is $(x-1)^2$, which is a polynomial and is defined for all real values of $x$.
Since the cube root of any real number is well-defined for all real numbers, the function $f(x)$ is defined for all $x \in \mathbb{R}$.
Therefore, the domain of the function is $(-\infty, \infty)$.
Answer: $(-\infty, \infty)$
The expression inside the cube root is $(x-1)^2$, which is a polynomial and is defined for all real values of $x$.
Since the cube root of any real number is well-defined for all real numbers, the function $f(x)$ is defined for all $x \in \mathbb{R}$.
Therefore, the domain of the function is $(-\infty, \infty)$.
Answer: $(-\infty, \infty)$
Hence, the correct answer is option: 'B'.