Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Let's define the composite function [tex]\(\left(\frac{q}{p}\right)(x)\)[/tex] as given by the problem statement.
To find [tex]\(\left(\frac{q}{p}\right)(x)\)[/tex], we need to use the functions [tex]\(q(x)\)[/tex] and [tex]\(p(x)\)[/tex] provided:
- [tex]\(p(x) = x^2 + 4x\)[/tex]
- [tex]\(q(x) = \sqrt{2 - x}\)[/tex]
The composite function [tex]\(\left(\frac{q}{p}\right)(x)\)[/tex] means we are dividing [tex]\(q(x)\)[/tex] by [tex]\(p(x)\)[/tex]. Therefore, the expression for [tex]\(\left(\frac{q}{p}\right)(x)\)[/tex] will be:
[tex]\[ \left(\frac{q}{p}\right)(x) = \frac{q(x)}{p(x)} \][/tex]
Plugging the expressions for [tex]\(q(x)\)[/tex] and [tex]\(p(x)\)[/tex] into this formula, we get:
[tex]\[ \left(\frac{q}{p}\right)(x) = \frac{\sqrt{2 - x}}{x^2 + 4x} \][/tex]
So, the required composite function [tex]\(\left(\frac{q}{p}\right)(x)\)[/tex] is:
[tex]\[ \left(\frac{q}{p}\right)(x) = \frac{\sqrt{2 - x}}{x^2 + 4x} \][/tex]
This is the expression for [tex]\(\left(\frac{q}{p}\right)(x)\)[/tex].
To find [tex]\(\left(\frac{q}{p}\right)(x)\)[/tex], we need to use the functions [tex]\(q(x)\)[/tex] and [tex]\(p(x)\)[/tex] provided:
- [tex]\(p(x) = x^2 + 4x\)[/tex]
- [tex]\(q(x) = \sqrt{2 - x}\)[/tex]
The composite function [tex]\(\left(\frac{q}{p}\right)(x)\)[/tex] means we are dividing [tex]\(q(x)\)[/tex] by [tex]\(p(x)\)[/tex]. Therefore, the expression for [tex]\(\left(\frac{q}{p}\right)(x)\)[/tex] will be:
[tex]\[ \left(\frac{q}{p}\right)(x) = \frac{q(x)}{p(x)} \][/tex]
Plugging the expressions for [tex]\(q(x)\)[/tex] and [tex]\(p(x)\)[/tex] into this formula, we get:
[tex]\[ \left(\frac{q}{p}\right)(x) = \frac{\sqrt{2 - x}}{x^2 + 4x} \][/tex]
So, the required composite function [tex]\(\left(\frac{q}{p}\right)(x)\)[/tex] is:
[tex]\[ \left(\frac{q}{p}\right)(x) = \frac{\sqrt{2 - x}}{x^2 + 4x} \][/tex]
This is the expression for [tex]\(\left(\frac{q}{p}\right)(x)\)[/tex].
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.