Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To find [tex]\( u(x) \)[/tex] given that [tex]\( q(x) = p(u(x)) \)[/tex], we can proceed as follows:
1. Define the given functions:
- [tex]\( p(x) = 8x - 3 \)[/tex]
- [tex]\( q(x) = \sqrt[5]{x} - 3 \)[/tex]
2. Express the relationship [tex]\( q(x) = p(u(x)) \)[/tex]:
[tex]\[ \sqrt[5]{x} - 3 = 8u(x) - 3 \][/tex]
3. Isolate [tex]\( u(x) \)[/tex]:
- First, eliminate the constant term [tex]\(-3\)[/tex] from both sides:
[tex]\[ \sqrt[5]{x} - 3 + 3 = 8u(x) - 3 + 3 \][/tex]
Simplifies to:
[tex]\[ \sqrt[5]{x} = 8u(x) \][/tex]
- Next, solve for [tex]\( u(x) \)[/tex]:
[tex]\[ u(x) = \frac{\sqrt[5]{x}}{8} \][/tex]
Hence, the function [tex]\( u(x) \)[/tex] is:
[tex]\[ u(x) = \frac{\sqrt[5]{x}}{8} \][/tex]
So, the answer is:
[tex]\[ u(x) = \boxed{\frac{\sqrt[5]{x}}{8}} \][/tex]
1. Define the given functions:
- [tex]\( p(x) = 8x - 3 \)[/tex]
- [tex]\( q(x) = \sqrt[5]{x} - 3 \)[/tex]
2. Express the relationship [tex]\( q(x) = p(u(x)) \)[/tex]:
[tex]\[ \sqrt[5]{x} - 3 = 8u(x) - 3 \][/tex]
3. Isolate [tex]\( u(x) \)[/tex]:
- First, eliminate the constant term [tex]\(-3\)[/tex] from both sides:
[tex]\[ \sqrt[5]{x} - 3 + 3 = 8u(x) - 3 + 3 \][/tex]
Simplifies to:
[tex]\[ \sqrt[5]{x} = 8u(x) \][/tex]
- Next, solve for [tex]\( u(x) \)[/tex]:
[tex]\[ u(x) = \frac{\sqrt[5]{x}}{8} \][/tex]
Hence, the function [tex]\( u(x) \)[/tex] is:
[tex]\[ u(x) = \frac{\sqrt[5]{x}}{8} \][/tex]
So, the answer is:
[tex]\[ u(x) = \boxed{\frac{\sqrt[5]{x}}{8}} \][/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.