To form correct pairs for the given functions [tex]\( f(x) = 1 - x^2 \)[/tex] and [tex]\( g(x) = \sqrt{11 - 4x} \)[/tex], let's evaluate each combined function at the specified points and match them with the given answers.
1. [tex]\((g - f)(-1)\)[/tex]
2. [tex]\((g + f)(2)\)[/tex]
3. [tex]\((g \cdot f)(2)\)[/tex]
4. [tex]\(\left(\frac{f}{g}\right)(-1)\)[/tex]
Using the values derived previously:
- [tex]\((g - f)(-1) = 3.872983346207417\)[/tex]
- [tex]\((g + f)(2) = -1.2679491924311228\)[/tex]
- [tex]\((g \cdot f)(2) = -5.196152422706632\)[/tex]
- [tex]\(\left(\frac{f}{g}\right)(-1) = 0.0\)[/tex]
Matching these values with the corresponding function evaluations:
- [tex]\((g - f)(-1) \rightarrow 3.872983346207417\)[/tex]
- [tex]\((g + f)(2) \rightarrow -1.2679491924311228\)[/tex]
- [tex]\((g \cdot f)(2) \rightarrow -5.196152422706632\)[/tex]
- [tex]\(\left(\frac{f}{g}\right)(-1) \rightarrow 0.0\)[/tex]
Now, let's form the correct pairs with the given numerical values:
- 0 → [tex]\(\left(\frac{f}{g}\right)(-1)\)[/tex]
- [tex]\(\sqrt{3} - 3\)[/tex] → [tex]\((g + f)(2)\)[/tex]
- [tex]\(0.0\)[/tex] → [tex]\((g - f)(-1)\)[/tex]
- [tex]\( -3 \sqrt{3}\)[/tex] → [tex]\((g \cdot f)(2)\)[/tex]
Therefore, the correct pairs for the combined functions and their corresponding values are:
1. [tex]\((g - f)(-1) \rightarrow 3.872983346207417\)[/tex]
2. [tex]\((g + f)(2) \rightarrow -1.2679491924311228\)[/tex]
3. [tex]\((g \cdot f)(2) \rightarrow -5.196152422706632\)[/tex]
4. [tex]\(\left(\frac{f}{g}\right)(-1) \rightarrow 0.0\)[/tex]
