At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Get precise and detailed answers to your questions from a knowledgeable community of experts on our 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.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
