Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To find \((f - g)(x)\) for the given functions \(f(x)\) and \(g(x)\), we perform the following steps:
1. Write down the given functions:
[tex]\[ f(x) = 2x^2 - 5 \][/tex]
[tex]\[ g(x) = x^2 - 4x - 8 \][/tex]
2. Subtract \(g(x)\) from \(f(x)\):
[tex]\[ (f - g)(x) = f(x) - g(x) \][/tex]
Substituting the expressions for \(f(x)\) and \(g(x)\), we get:
[tex]\[ (f - g)(x) = (2x^2 - 5) - (x^2 - 4x - 8) \][/tex]
3. Distribute the negative sign and combine like terms:
[tex]\[ (f - g)(x) = 2x^2 - 5 - x^2 + 4x + 8 \][/tex]
4. Simplify the expression by combining like terms:
- Combine the \(x^2\) terms:
[tex]\[ 2x^2 - x^2 = x^2 \][/tex]
- The \(x\) terms remain as is:
[tex]\[ +4x \][/tex]
- Combine the constant terms:
[tex]\[ -5 + 8 = 3 \][/tex]
So, the simplified expression is:
[tex]\[ (f - g)(x) = x^2 + 4x + 3 \][/tex]
5. Check the multiple-choice options:
- A. \(x^2 - 4x - 3\)
- B. \(x^2 + 4x + 3\)
- C. \(-x^2 - 13\)
- D. \(3x^2 - 4x - 13\)
The correct expression \((f - g)(x)\) which we found is \(x^2 + 4x + 3\).
Thus, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
1. Write down the given functions:
[tex]\[ f(x) = 2x^2 - 5 \][/tex]
[tex]\[ g(x) = x^2 - 4x - 8 \][/tex]
2. Subtract \(g(x)\) from \(f(x)\):
[tex]\[ (f - g)(x) = f(x) - g(x) \][/tex]
Substituting the expressions for \(f(x)\) and \(g(x)\), we get:
[tex]\[ (f - g)(x) = (2x^2 - 5) - (x^2 - 4x - 8) \][/tex]
3. Distribute the negative sign and combine like terms:
[tex]\[ (f - g)(x) = 2x^2 - 5 - x^2 + 4x + 8 \][/tex]
4. Simplify the expression by combining like terms:
- Combine the \(x^2\) terms:
[tex]\[ 2x^2 - x^2 = x^2 \][/tex]
- The \(x\) terms remain as is:
[tex]\[ +4x \][/tex]
- Combine the constant terms:
[tex]\[ -5 + 8 = 3 \][/tex]
So, the simplified expression is:
[tex]\[ (f - g)(x) = x^2 + 4x + 3 \][/tex]
5. Check the multiple-choice options:
- A. \(x^2 - 4x - 3\)
- B. \(x^2 + 4x + 3\)
- C. \(-x^2 - 13\)
- D. \(3x^2 - 4x - 13\)
The correct expression \((f - g)(x)\) which we found is \(x^2 + 4x + 3\).
Thus, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.