Get the answers you need from a community of experts on IDNLearn.com. Find in-depth and trustworthy answers to all your questions from our experienced community members.
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].
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.
