We appreciate your visit to 3 Find tex f cdot g x tex if tex f x 7x 3 5x 2 42x 30 tex and tex g x 7x 5. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find [tex]\((f \cdot g)(x)\)[/tex], where [tex]\(f(x) = 7x^3 - 5x^2 + 42x - 30\)[/tex] and [tex]\(g(x) = 7x - 5\)[/tex], we need to multiply the two functions together. Let's go through the steps:
1. Set Up the Multiplication:
We need to multiply each term of [tex]\(f(x)\)[/tex] by each term of [tex]\(g(x)\)[/tex]. This means calculating each term generated by multiplying terms from [tex]\(f(x)\)[/tex] with the term from [tex]\(g(x)\)[/tex]:
[tex]\[
(7x^3 - 5x^2 + 42x - 30) \cdot (7x - 5)
\][/tex]
2. Distribute the Terms:
- Multiply [tex]\(7x^3\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
[tex]\[
7x^3 \cdot 7x = 49x^4
\][/tex]
[tex]\[
7x^3 \cdot (-5) = -35x^3
\][/tex]
- Multiply [tex]\(-5x^2\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
[tex]\[
-5x^2 \cdot 7x = -35x^3
\][/tex]
[tex]\[
-5x^2 \cdot (-5) = 25x^2
\][/tex]
- Multiply [tex]\(42x\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
[tex]\[
42x \cdot 7x = 294x^2
\][/tex]
[tex]\[
42x \cdot (-5) = -210x
\][/tex]
- Multiply [tex]\(-30\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
[tex]\[
-30 \cdot 7x = -210x
\][/tex]
[tex]\[
-30 \cdot (-5) = 150
\][/tex]
3. Combine All Terms:
Now, add all the terms together:
[tex]\[
49x^4 + (-35x^3 - 35x^3) + (25x^2 + 294x^2) + (-210x - 210x) + 150
\][/tex]
4. Simplify:
- Combine like terms:
[tex]\[
49x^4 - 70x^3 + 319x^2 - 420x + 150
\][/tex]
So, [tex]\((f \cdot g)(x) = 49x^4 - 70x^3 + 319x^2 - 420x + 150\)[/tex].
This matches with the given options, making the correct choice: [tex]\(49x^4 - 70x^3 + 319x^2 - 420x + 150\)[/tex].
1. Set Up the Multiplication:
We need to multiply each term of [tex]\(f(x)\)[/tex] by each term of [tex]\(g(x)\)[/tex]. This means calculating each term generated by multiplying terms from [tex]\(f(x)\)[/tex] with the term from [tex]\(g(x)\)[/tex]:
[tex]\[
(7x^3 - 5x^2 + 42x - 30) \cdot (7x - 5)
\][/tex]
2. Distribute the Terms:
- Multiply [tex]\(7x^3\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
[tex]\[
7x^3 \cdot 7x = 49x^4
\][/tex]
[tex]\[
7x^3 \cdot (-5) = -35x^3
\][/tex]
- Multiply [tex]\(-5x^2\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
[tex]\[
-5x^2 \cdot 7x = -35x^3
\][/tex]
[tex]\[
-5x^2 \cdot (-5) = 25x^2
\][/tex]
- Multiply [tex]\(42x\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
[tex]\[
42x \cdot 7x = 294x^2
\][/tex]
[tex]\[
42x \cdot (-5) = -210x
\][/tex]
- Multiply [tex]\(-30\)[/tex] by each term in [tex]\(g(x)\)[/tex]:
[tex]\[
-30 \cdot 7x = -210x
\][/tex]
[tex]\[
-30 \cdot (-5) = 150
\][/tex]
3. Combine All Terms:
Now, add all the terms together:
[tex]\[
49x^4 + (-35x^3 - 35x^3) + (25x^2 + 294x^2) + (-210x - 210x) + 150
\][/tex]
4. Simplify:
- Combine like terms:
[tex]\[
49x^4 - 70x^3 + 319x^2 - 420x + 150
\][/tex]
So, [tex]\((f \cdot g)(x) = 49x^4 - 70x^3 + 319x^2 - 420x + 150\)[/tex].
This matches with the given options, making the correct choice: [tex]\(49x^4 - 70x^3 + 319x^2 - 420x + 150\)[/tex].
Thanks for taking the time to read 3 Find tex f cdot g x tex if tex f x 7x 3 5x 2 42x 30 tex and tex g x 7x 5. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
