Answer:
The equivalent functions are;
[tex]g(x) = 3^{-2 \cdot x }[/tex]
[tex]g(x) = 9^{-x}[/tex]
[tex]g(x) = \left (\dfrac{1}{9} \right )^x[/tex]
Step-by-step explanation:
The given function is f(x) = (1/3)^(2·x)
[tex]f(x) = \dfrac{1}{3} ^{2 \cdot x}[/tex]
The given function can be simplified as follows;
[tex]f(x) = \dfrac{1}{3} ^{2 \cdot x} = 3^{-1 \cdot2 \cdot x } = 3^{-2 \cdot x } = g(x)[/tex]
∴ [tex]f(x) = \dfrac{1}{3} ^{2 \cdot x}[/tex] ≡ [tex]g(x) = 3^{-2 \cdot x }[/tex]
2) The given function can also be simplified as follows;
[tex]f(x) = \dfrac{1}{3} ^{2 \cdot x} = \left (\dfrac{1}{3} ^2\right )^x = \left (\dfrac{1}{9} \right )^x = (9^{-1}) ^x} = 9^{-1 \times x} = 9^{-x} = g(x)[/tex]
∴ [tex]f(x) = \dfrac{1}{3} ^{2 \cdot x}[/tex] ≡ [tex]g(x) = 9^{-x}[/tex]
3) The given function can also be simplified as follows;
[tex]f(x) = \dfrac{1}{3} ^{2 \cdot x} = \left (\dfrac{1}{3} ^2\right )^x = \left (\dfrac{1}{9} \right )^x = g(x)[/tex]
∴ [tex]f(x) = \dfrac{1}{3} ^{2 \cdot x}[/tex] ≡ [tex]g(x) = \left (\dfrac{1}{9} \right )^x[/tex]
