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Sagot :
Given:
The function is
[tex]g(x)=(\dfrac{1}{5})^x[/tex]
To find:
The correct ordered pairs.
Solution:
We have,
[tex]g(x)=(\dfrac{1}{5})^x[/tex]
For x=3,
[tex]g(3)=(\dfrac{1}{5})^3[/tex]
[tex]g(3)=\dfrac{1}{125}[/tex]
So, the ordered pair is [tex](3,\dfrac{1}{125})[/tex].
For x=-2,
[tex]g(-2)=(\dfrac{1}{5})^{-2}[/tex]
[tex]g(-2)=(5)^2[/tex] [tex][\because (\dfrac{a}{b})^{-n}=(\dfrac{b}{a})^n][/tex]
[tex]g(-2)=25[/tex]
So, the ordered pair is [tex](-2,25)[/tex].
For x=1,
[tex]g(1)=(\dfrac{1}{5})^1[/tex]
[tex]g(1)=\dfrac{1}{5}[/tex]
So, the ordered pair is [tex](1,\dfrac{1}{5})[/tex].
For x=-1,
[tex]g(-1)=(\dfrac{1}{5})^{-1}[/tex]
[tex]g(-1)=(5)^1[/tex] [tex][\because (\dfrac{a}{b})^{-n}=(\dfrac{b}{a})^n][/tex]
[tex]g(-1)=5[/tex]
So, the ordered pair is (-1,5). This is the correct answer.
Therefore, the correct option is D.
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