Answered

Get the answers you've been looking for with the help of IDNLearn.com's expert community. Discover reliable answers to your questions with our extensive database of expert knowledge.

Drag the tiles to the boxes to form correct pairs.

Consider functions [tex]f[/tex] and [tex]g[/tex].

[tex]\[
\begin{array}{l}
f(x)=1-x^2 \\
g(x)=\sqrt{11-4x}
\end{array}
\][/tex]

Evaluate each combined function, and match it to the corresponding value.

0 [tex]\[\square\][/tex]

[tex]\(\sqrt{3}-3\)[/tex] [tex]\[\square\][/tex]

-3\sqrt{3} [tex]\[\square\][/tex]

(g-f)(-1) [tex]\[\qquad\][/tex] [tex]\[\square\][/tex]

(g+f)(2) [tex]\[\qquad\][/tex] [tex]\[\square\][/tex]

(g \cdot f)(2) [tex]\[\qquad\][/tex] [tex]\[\square\][/tex]

[tex]\(\left(\frac{f}{g}\right)(-1)\)[/tex] [tex]\[\longrightarrow\][/tex] [tex]\[\square\][/tex]

Sagot :

GinnyAnsweridn
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]
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.