Question

PLEASE PLEASE HELP MEE!!

Answer 1

Answer:

The equivalent functions are;

$g(x) = 3^{-2 \cdot x }$

$g(x) = 9^{-x}$

$g(x) = \left (\dfrac{1}{9} \right )^x$

Step-by-step explanation:

The given function is f(x) = (1/3)^(2·x)

$f(x) = \dfrac{1}{3} ^{2 \cdot x}$

The given  function can be simplified as follows;

$f(x) = \dfrac{1}{3} ^{2 \cdot x} = 3^{-1 \cdot2 \cdot x } = 3^{-2 \cdot x } = g(x)$

∴ $f(x) = \dfrac{1}{3} ^{2 \cdot x}$ ≡  $g(x) = 3^{-2 \cdot x }$

2) The given  function can also be simplified as follows;

$f(x) = \dfrac{1}{3} ^{2 \cdot x} = \left (\dfrac{1}{3} ^2\right )^x = \left (\dfrac{1}{9} \right )^x = (9^{-1}) ^x} = 9^{-1 \times x} = 9^{-x} = g(x)$

∴ $f(x) = \dfrac{1}{3} ^{2 \cdot x}$ ≡ $g(x) = 9^{-x}$

3) The given  function can also be simplified as follows;

$f(x) = \dfrac{1}{3} ^{2 \cdot x} = \left (\dfrac{1}{3} ^2\right )^x = \left (\dfrac{1}{9} \right )^x = g(x)$

∴ $f(x) = \dfrac{1}{3} ^{2 \cdot x}$ ≡ $g(x) = \left (\dfrac{1}{9} \right )^x$