Pregunta
Which of the following does not represent the domain of the function
\( g(x)=-\sqrt[3]{x}+5 \) ?
Option \#1: \( (-\infty, \infty) \)
Option \#2:- \( -\infty
Ask by Johnson Bolton. in the United States
Jan 23,2025
Ask by Johnson Bolton. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The best answer is Option #3.
Solución
The best answer is Option #3.
**Explanation:**
- **Option #1:** \( (-\infty, \infty) \) correctly represents all real numbers.
- **Option #2:** \( -\infty < x < \infty \) also correctly represents all real numbers.
- **Option #3:** \( [-\infty, \infty] \) is incorrect because infinity (\( \infty \)) is not a real number and cannot be included in an interval using square brackets.
**Answer:** Option #3
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Simplifique esta solución Mind Expander
The best answer is Option \# 3. While both Option \#1 and Option \#2 effectively describe the full domain of the function \( g(x) = -\sqrt[3]{x} + 5 \), which is all real numbers, Option \#3 includes an incorrect use of the interval notation by adding brackets that imply a closed interval including infinity, which is not possible. In this function, since the cube root function can take any real number as input, the domain is indeed all real numbers. Therefore, you can plug in any value for \( x \) without restriction!
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