Find answers to your most challenging questions with the help of IDNLearn.com's experts. Join our community to receive prompt, thorough responses from knowledgeable experts.
Sagot :
To determine which function can take the value of [tex]\(-4\)[/tex], we'll analyze each function and see if setting [tex]\( y = -4 \)[/tex] yields a valid solution for [tex]\( x \)[/tex].
1. Function: [tex]\(y = \sqrt{x} - 5\)[/tex]
- To find out if [tex]\( -4 \)[/tex] is in the range:
[tex]\[ y = -4 \implies -4 = \sqrt{x} - 5 \][/tex]
- Solving for [tex]\( x \)[/tex]:
[tex]\[ -4 + 5 = \sqrt{x} \implies 1 = \sqrt{x} \implies x = 1 \][/tex]
- Since [tex]\( x = 1 \)[/tex] is a valid number, [tex]\( y = \sqrt{x} - 5 \)[/tex] can indeed be [tex]\(-4\)[/tex]. Thus, [tex]\(-4\)[/tex] is in the range of [tex]\( y = \sqrt{x} - 5 \)[/tex].
2. Function: [tex]\(y = \sqrt{x} + 5\)[/tex]
- To find out if [tex]\( -4 \)[/tex] is in the range:
[tex]\[ y = -4 \implies -4 = \sqrt{x} + 5 \][/tex]
- Solving for [tex]\( x \)[/tex]:
[tex]\[ -4 - 5 = \sqrt{x} \implies -9 = \sqrt{x} \][/tex]
- Since the square root of a number is always non-negative, [tex]\(\sqrt{x} = -9\)[/tex] is impossible. Therefore, [tex]\(-4\)[/tex] is not in the range of [tex]\( y = \sqrt{x} + 5 \)[/tex].
3. Function: [tex]\(y = \sqrt{x+5}\)[/tex]
- To find out if [tex]\( -4 \)[/tex] is in the range:
[tex]\[ y = -4 \implies -4 = \sqrt{x+5} \][/tex]
- Solving for [tex]\( x \)[/tex]:
[tex]\[ -4 = \sqrt{x + 5} \][/tex]
- As the square root function returns a non-negative value, [tex]\(-4 = \sqrt{x + 5}\)[/tex] is impossible. Therefore, [tex]\(-4\)[/tex] is not in the range of [tex]\( y = \sqrt{x+5} \)[/tex].
4. Function: [tex]\(y = \sqrt{x-5}\)[/tex]
- To find out if [tex]\( -4 \)[/tex] is in the range:
[tex]\[ y = -4 \implies -4 = \sqrt{x-5} \][/tex]
- Solving for [tex]\( x \)[/tex]:
[tex]\[ -4 = \sqrt{x - 5} \][/tex]
- Similarly, since the square root function returns a non-negative value, [tex]\(-4 = \sqrt{x - 5}\)[/tex] is impossible. Therefore, [tex]\(-4\)[/tex] is not in the range of [tex]\( y = \sqrt{x-5} \)[/tex].
After analyzing each function, we determine that the function [tex]\( y = \sqrt{x} - 5 \)[/tex] is the only one whose range includes [tex]\(-4\)[/tex].
1. Function: [tex]\(y = \sqrt{x} - 5\)[/tex]
- To find out if [tex]\( -4 \)[/tex] is in the range:
[tex]\[ y = -4 \implies -4 = \sqrt{x} - 5 \][/tex]
- Solving for [tex]\( x \)[/tex]:
[tex]\[ -4 + 5 = \sqrt{x} \implies 1 = \sqrt{x} \implies x = 1 \][/tex]
- Since [tex]\( x = 1 \)[/tex] is a valid number, [tex]\( y = \sqrt{x} - 5 \)[/tex] can indeed be [tex]\(-4\)[/tex]. Thus, [tex]\(-4\)[/tex] is in the range of [tex]\( y = \sqrt{x} - 5 \)[/tex].
2. Function: [tex]\(y = \sqrt{x} + 5\)[/tex]
- To find out if [tex]\( -4 \)[/tex] is in the range:
[tex]\[ y = -4 \implies -4 = \sqrt{x} + 5 \][/tex]
- Solving for [tex]\( x \)[/tex]:
[tex]\[ -4 - 5 = \sqrt{x} \implies -9 = \sqrt{x} \][/tex]
- Since the square root of a number is always non-negative, [tex]\(\sqrt{x} = -9\)[/tex] is impossible. Therefore, [tex]\(-4\)[/tex] is not in the range of [tex]\( y = \sqrt{x} + 5 \)[/tex].
3. Function: [tex]\(y = \sqrt{x+5}\)[/tex]
- To find out if [tex]\( -4 \)[/tex] is in the range:
[tex]\[ y = -4 \implies -4 = \sqrt{x+5} \][/tex]
- Solving for [tex]\( x \)[/tex]:
[tex]\[ -4 = \sqrt{x + 5} \][/tex]
- As the square root function returns a non-negative value, [tex]\(-4 = \sqrt{x + 5}\)[/tex] is impossible. Therefore, [tex]\(-4\)[/tex] is not in the range of [tex]\( y = \sqrt{x+5} \)[/tex].
4. Function: [tex]\(y = \sqrt{x-5}\)[/tex]
- To find out if [tex]\( -4 \)[/tex] is in the range:
[tex]\[ y = -4 \implies -4 = \sqrt{x-5} \][/tex]
- Solving for [tex]\( x \)[/tex]:
[tex]\[ -4 = \sqrt{x - 5} \][/tex]
- Similarly, since the square root function returns a non-negative value, [tex]\(-4 = \sqrt{x - 5}\)[/tex] is impossible. Therefore, [tex]\(-4\)[/tex] is not in the range of [tex]\( y = \sqrt{x-5} \)[/tex].
After analyzing each function, we determine that the function [tex]\( y = \sqrt{x} - 5 \)[/tex] is the only one whose range includes [tex]\(-4\)[/tex].
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.
