Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
To find [tex]\(f(x) + g(x)\)[/tex] given the functions [tex]\(f(x) = x^3 - 2x^2 + 3x - 5\)[/tex] and [tex]\(g(x) = x^2 + x - 1\)[/tex], we need to perform the addition of these two functions.
Here are the steps:
1. Write down the functions:
[tex]\[ f(x) = x^3 - 2x^2 + 3x - 5 \][/tex]
[tex]\[ g(x) = x^2 + x - 1 \][/tex]
2. Perform the addition [tex]\(f(x) + g(x)\)[/tex] by combining like terms:
[tex]\[ f(x) + g(x) = (x^3 - 2x^2 + 3x - 5) + (x^2 + x - 1) \][/tex]
3. Combine the corresponding terms for each power of [tex]\(x\)[/tex]:
[tex]\[ = x^3 + (-2x^2 + x^2) + (3x + x) + (-5 - 1) \][/tex]
4. Simplify each group of like terms:
[tex]\[ x^3 + (-2x^2 + x^2) + (3x + x) + (-5 - 1) \][/tex]
- Combine [tex]\(x^2\)[/tex] terms: [tex]\(-2x^2 + x^2 = -x^2\)[/tex]
- Combine [tex]\(x\)[/tex] terms: [tex]\(3x + x = 4x\)[/tex]
- Combine constant terms: [tex]\(-5 - 1 = -6\)[/tex]
5. Write down the simplified result:
[tex]\[ f(x) + g(x) = x^3 - x^2 + 4x - 6 \][/tex]
6. Therefore, the final result of the function operation [tex]\(f(x) + g(x)\)[/tex] is:
[tex]\[ f(x) + g(x) = x^3 - x^2 + 4x - 6 \][/tex]
Here are the steps:
1. Write down the functions:
[tex]\[ f(x) = x^3 - 2x^2 + 3x - 5 \][/tex]
[tex]\[ g(x) = x^2 + x - 1 \][/tex]
2. Perform the addition [tex]\(f(x) + g(x)\)[/tex] by combining like terms:
[tex]\[ f(x) + g(x) = (x^3 - 2x^2 + 3x - 5) + (x^2 + x - 1) \][/tex]
3. Combine the corresponding terms for each power of [tex]\(x\)[/tex]:
[tex]\[ = x^3 + (-2x^2 + x^2) + (3x + x) + (-5 - 1) \][/tex]
4. Simplify each group of like terms:
[tex]\[ x^3 + (-2x^2 + x^2) + (3x + x) + (-5 - 1) \][/tex]
- Combine [tex]\(x^2\)[/tex] terms: [tex]\(-2x^2 + x^2 = -x^2\)[/tex]
- Combine [tex]\(x\)[/tex] terms: [tex]\(3x + x = 4x\)[/tex]
- Combine constant terms: [tex]\(-5 - 1 = -6\)[/tex]
5. Write down the simplified result:
[tex]\[ f(x) + g(x) = x^3 - x^2 + 4x - 6 \][/tex]
6. Therefore, the final result of the function operation [tex]\(f(x) + g(x)\)[/tex] is:
[tex]\[ f(x) + g(x) = x^3 - x^2 + 4x - 6 \][/tex]
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. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.