At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Alright, let's delve into the given function [tex]\( f(x) \)[/tex] and understand its various components step-by-step.
The function in question is:
[tex]\[ f(x) = \sqrt{2x} + 5x^2 \][/tex]
### Step-by-Step Solution:
1. Understand Each Term:
- The first term is [tex]\( \sqrt{2x} \)[/tex], which involves a square root of the product of 2 and [tex]\( x \)[/tex].
- The second term is [tex]\( 5x^2 \)[/tex], which is a basic polynomial term where [tex]\( x \)[/tex] is squared and then multiplied by 5.
2. Rewrite the Function:
Let's rewrite the function to clearly see its structure:
[tex]\[ f(x) = \sqrt{2x} + 5x^2 \][/tex]
3. Handling the Square Root Term:
Consider the first term [tex]\( \sqrt{2x} \)[/tex]:
- The expression [tex]\( 2x \)[/tex] is inside the square root. To manipulate or simplify this, remember that:
[tex]\[ \sqrt{2x} = \sqrt{2} \cdot \sqrt{x} \][/tex]
Thus, we separate it into two distinct square root factors.
4. Handling the Polynomial Term:
The second term [tex]\( 5x^2 \)[/tex] is already in its simplest form:
- [tex]\( 5 \)[/tex] is the coefficient.
- [tex]\( x^2 \)[/tex] is [tex]\( x \)[/tex] raised to the power of 2.
So, combining both observations, we can rewrite the function as:
[tex]\[ f(x) = \sqrt{2} \cdot \sqrt{x} + 5x^2 \][/tex]
However, this expression:
[tex]\[ \sqrt{2}\sqrt{x} + 5x^2 \][/tex]
is more commonly written in a slightly more compact form:
[tex]\[ f(x) = \sqrt{2x} + 5x^2 \][/tex]
### Conclusion
In summary, the function [tex]\( f(x) \)[/tex] combines a radical expression and a polynomial expression:
[tex]\[ f(x) = \sqrt{2} \cdot \sqrt{x} + 5x^2 \][/tex]
Given this function:
[tex]\[ f(x) = \sqrt{2x} + 5x^2 \][/tex]
we recognize it can also be written as:
[tex]\[ f(x) = \sqrt{2}\sqrt{x} + 5x^2 \][/tex]
stressing the separate nature of the constants and variables involved.
The function in question is:
[tex]\[ f(x) = \sqrt{2x} + 5x^2 \][/tex]
### Step-by-Step Solution:
1. Understand Each Term:
- The first term is [tex]\( \sqrt{2x} \)[/tex], which involves a square root of the product of 2 and [tex]\( x \)[/tex].
- The second term is [tex]\( 5x^2 \)[/tex], which is a basic polynomial term where [tex]\( x \)[/tex] is squared and then multiplied by 5.
2. Rewrite the Function:
Let's rewrite the function to clearly see its structure:
[tex]\[ f(x) = \sqrt{2x} + 5x^2 \][/tex]
3. Handling the Square Root Term:
Consider the first term [tex]\( \sqrt{2x} \)[/tex]:
- The expression [tex]\( 2x \)[/tex] is inside the square root. To manipulate or simplify this, remember that:
[tex]\[ \sqrt{2x} = \sqrt{2} \cdot \sqrt{x} \][/tex]
Thus, we separate it into two distinct square root factors.
4. Handling the Polynomial Term:
The second term [tex]\( 5x^2 \)[/tex] is already in its simplest form:
- [tex]\( 5 \)[/tex] is the coefficient.
- [tex]\( x^2 \)[/tex] is [tex]\( x \)[/tex] raised to the power of 2.
So, combining both observations, we can rewrite the function as:
[tex]\[ f(x) = \sqrt{2} \cdot \sqrt{x} + 5x^2 \][/tex]
However, this expression:
[tex]\[ \sqrt{2}\sqrt{x} + 5x^2 \][/tex]
is more commonly written in a slightly more compact form:
[tex]\[ f(x) = \sqrt{2x} + 5x^2 \][/tex]
### Conclusion
In summary, the function [tex]\( f(x) \)[/tex] combines a radical expression and a polynomial expression:
[tex]\[ f(x) = \sqrt{2} \cdot \sqrt{x} + 5x^2 \][/tex]
Given this function:
[tex]\[ f(x) = \sqrt{2x} + 5x^2 \][/tex]
we recognize it can also be written as:
[tex]\[ f(x) = \sqrt{2}\sqrt{x} + 5x^2 \][/tex]
stressing the separate nature of the constants and variables involved.
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.