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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.

[tex]\sqrt{3} - 3[/tex]
[tex]\sqrt{15}[/tex]
[tex]-3 \sqrt{3}[/tex]
[tex]0[/tex]

[tex]
\begin{array}{l}
\left(\frac{f}{g}\right)(-1) \longrightarrow \\
(g+f)(2) \longrightarrow \\
(g-f)(-1) \longrightarrow \\
(g \cdot f)(2) \longrightarrow \\
\end{array}
[/tex]


Sagot :

To evaluate each combined function and match it to the corresponding value, let's look at each function step-by-step:

1. Evaluate [tex]\(\left(\frac{f}{g}\right)(-1)\)[/tex]:
[tex]$ f(x) = 1 - x^2 $[/tex]
[tex]$ f(-1) = 1 - (-1)^2 = 1 - 1 = 0 $[/tex]

[tex]$ g(x) = \sqrt{11 - 4x} $[/tex]
[tex]$ g(-1) = \sqrt{11 - 4(-1)} = \sqrt{11 + 4} = \sqrt{15} $[/tex]

[tex]$ \left(\frac{f}{g}\right)(-1) = \frac{f(-1)}{g(-1)} = \frac{0}{\sqrt{15}} = 0 $[/tex]

The combined function [tex]\(\left(\frac{f}{g}\right)(-1)\)[/tex] corresponds to [tex]\(0\)[/tex].

2. Evaluate [tex]\((g + f)(2)\)[/tex]:
[tex]$ f(2) = 1 - 2^2 = 1 - 4 = -3 $[/tex]

[tex]$ g(2) = \sqrt{11 - 4(2)} = \sqrt{11 - 8} = \sqrt{3} $[/tex]

[tex]$ (g + f)(2) = g(2) + f(2) = \sqrt{3} - 3 $[/tex]

The combined function [tex]\((g + f)(2)\)[/tex] corresponds to [tex]\(\sqrt{3} - 3\)[/tex].

3. Evaluate [tex]\((g - f)(-1)\)[/tex]:
We've already found [tex]\( f(-1) = 0 \)[/tex] and [tex]\( g(-1) = \sqrt{15} \)[/tex].

[tex]$ (g - f)(-1) = g(-1) - f(-1) = \sqrt{15} - 0 = \sqrt{15} $[/tex]

The combined function [tex]\((g - f)(-1)\)[/tex] corresponds to [tex]\(\sqrt{15}\)[/tex].

4. Evaluate [tex]\((g \cdot f)(2)\)[/tex]:
We've already found [tex]\( f(2) = -3 \)[/tex] and [tex]\( g(2) = \sqrt{3} \)[/tex].

[tex]$ (g \cdot f)(2) = g(2) \cdot f(2) = \sqrt{3} \cdot (-3) = -3\sqrt{3} $[/tex]

The combined function [tex]\((g \cdot f)(2)\)[/tex] corresponds to [tex]\(-3\sqrt{3}\)[/tex].

Putting it all together, we get the following pairs:

[tex]\[ \begin{array}{ll} \left(\frac{f}{g}\right)(-1) & \longrightarrow 0 \\ (g + f)(2) & \longrightarrow \sqrt{3} - 3 \\ (g - f)(-1) & \longrightarrow \sqrt{15} \\ (g \cdot f)(2) & \longrightarrow -3\sqrt{3} \\ \end{array} \][/tex]