Let's carefully analyze how each function combination relates to the given expressions using the numerical results provided.
1. Sum of the functions (f+g)(x):
According to the results:
[tex]\[(f + g)(3) = -42\][/tex]
2. Difference of the functions (f-g)(x):
According to the results:
[tex]\[(f - g)(3) = -30\][/tex]
3. Product of the functions (f·g)(x):
According to the results:
[tex]\[(f·g)(3) = 216\][/tex]
4. Quotient of the functions [tex]\(\left(\frac{f}{g}\right)(x)\)[/tex]:
According to the results:
[tex]\[\left(\frac{f}{g}\right)(3) = 6.0\][/tex]
Given the expressions:
1. [tex]\(x^2-7x-18\)[/tex]
2. [tex]\(x+3\)[/tex]
3. [tex]\(x^3-15 x^2 + 27x + 243\)[/tex]
Let's match them one by one:
- For [tex]\(x^2-7x-18\)[/tex], it seems to be a combination of a quadratic functions, suggesting sums or differences.
- For [tex]\(x+3\)[/tex], which is linear, suggesting simplified quotient or difference.
- For [tex]\(x^3-15x^2+27x+243\)[/tex], this clearly looks like a polynomial of higher degree, typical for products.
So we conclude:
- [tex]\(x^2-7 x-18\)[/tex] matches with [tex]\((f+g)(x)\)[/tex] since
- [tex]\(x+3\)[/tex] matches with [tex]\(\left(\frac{f}{g}\right)(x)\)[/tex]
- [tex]\(x^3-15x^2+27x+243\)[/tex] matches with [tex]\((f·g)(x)\)[/tex]
Let's drag and match the correct boxes:
- [tex]\( (f+g)(x) \)[/tex] ⟶ [tex]\( x^2-7 x-18 \)[/tex]
- [tex]\( (f-g)(x) \)[/tex] ⟶
- [tex]\( (f·g)(x) \)[/tex] ⟶ [tex]\( x^3-15 x^2 + 27x + 243\)[/tex]
- [tex]\( \left(\frac{f}{g}\right)(x) \)[/tex] ⟶ [tex]\( x+3 \)[/tex]
Hence:
- [tex]\((f+g)(x) \quad x^2-7 x-18\)[/tex]
- [tex]\( (f-g)(x) \)[/tex]
- [tex]\((f·g)(x) \quad x^3-15 x^2 + 27x + 243\)[/tex]
- [tex]\( \left(\frac{f}{g}\right)(x) \quad x+3\)[/tex]
