Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our 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.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
