Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To determine the domain of the function [tex]\( y = \sqrt{x} \)[/tex], we need to consider the properties of the square root function.
The square root function is defined for all non-negative real numbers. This means that the value inside the square root (i.e., [tex]\( x \)[/tex]) must be greater than or equal to zero. In other words, [tex]\( \sqrt{x} \)[/tex] is defined if and only if [tex]\( x \geq 0 \)[/tex].
Let’s now analyze the four options given to see which one correctly describes this condition:
1. [tex]\( -\infty < x < \infty \)[/tex]: This option suggests that [tex]\( x \)[/tex] can be any real number, including negative values. However, [tex]\( \sqrt{x} \)[/tex] is not defined for negative values of [tex]\( x \)[/tex]. Therefore, this option is incorrect.
2. [tex]\( 0 < x < \infty \)[/tex]: This option suggests that [tex]\( x \)[/tex] must be positive but not zero. However, [tex]\( \sqrt{x} \)[/tex] is defined for [tex]\( x = 0 \)[/tex] because [tex]\( \sqrt{0} = 0 \)[/tex]. Therefore, this option is not entirely correct because it excludes zero.
3. [tex]\( 0 \leq x < \infty \)[/tex]: This option includes all non-negative real numbers, starting from zero and extending to infinity. Since [tex]\( \sqrt{x} \)[/tex] is defined for all [tex]\( x \)[/tex] in this range, this option correctly represents the domain of the function.
4. [tex]\( 1 \leq x < \infty \)[/tex]: This option suggests that [tex]\( x \)[/tex] must be greater than or equal to 1. This excludes all values from 0 to 1, which are part of the domain of [tex]\( \sqrt{x} \)[/tex]. Therefore, this option is incorrect.
Thus, the correct domain of the function [tex]\( y = \sqrt{x} \)[/tex] is [tex]\( 0 \leq x < \infty \)[/tex].
The correct answer is:
[tex]\[ \boxed{0 \leq x < \infty} \][/tex]
The square root function is defined for all non-negative real numbers. This means that the value inside the square root (i.e., [tex]\( x \)[/tex]) must be greater than or equal to zero. In other words, [tex]\( \sqrt{x} \)[/tex] is defined if and only if [tex]\( x \geq 0 \)[/tex].
Let’s now analyze the four options given to see which one correctly describes this condition:
1. [tex]\( -\infty < x < \infty \)[/tex]: This option suggests that [tex]\( x \)[/tex] can be any real number, including negative values. However, [tex]\( \sqrt{x} \)[/tex] is not defined for negative values of [tex]\( x \)[/tex]. Therefore, this option is incorrect.
2. [tex]\( 0 < x < \infty \)[/tex]: This option suggests that [tex]\( x \)[/tex] must be positive but not zero. However, [tex]\( \sqrt{x} \)[/tex] is defined for [tex]\( x = 0 \)[/tex] because [tex]\( \sqrt{0} = 0 \)[/tex]. Therefore, this option is not entirely correct because it excludes zero.
3. [tex]\( 0 \leq x < \infty \)[/tex]: This option includes all non-negative real numbers, starting from zero and extending to infinity. Since [tex]\( \sqrt{x} \)[/tex] is defined for all [tex]\( x \)[/tex] in this range, this option correctly represents the domain of the function.
4. [tex]\( 1 \leq x < \infty \)[/tex]: This option suggests that [tex]\( x \)[/tex] must be greater than or equal to 1. This excludes all values from 0 to 1, which are part of the domain of [tex]\( \sqrt{x} \)[/tex]. Therefore, this option is incorrect.
Thus, the correct domain of the function [tex]\( y = \sqrt{x} \)[/tex] is [tex]\( 0 \leq x < \infty \)[/tex].
The correct answer is:
[tex]\[ \boxed{0 \leq x < \infty} \][/tex]
Answer:
A.
Step-by-step explanation:
The square root can be any value between negative intinity and positive infinity.
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.