Question

PLEASE PLEASE HELP MEE!!

Answer 1

The equivalent functions are;

`g(x) = 3^(-2 \cdot x )`

`g(x) = 9^(-x)`

`g(x) = \left ((1)/(9) \right )^x`

Explanation:

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

`f(x) = (1)/(3) ^(2 \cdot x)`

The given function can be simplified as follows;

`f(x) = (1)/(3) ^(2 \cdot x) = 3^(-1 \cdot2 \cdot x ) = 3^(-2 \cdot x ) = g(x)`

∴
`f(x) = (1)/(3) ^(2 \cdot x)` ≡
`g(x) = 3^(-2 \cdot x )`

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

`f(x) = (1)/(3) ^(2 \cdot x) = \left ((1)/(3) ^2\right )^x = \left ((1)/(9) \right )^x = (9^(-1)) ^x} = 9^(-1 * x) = 9^(-x) = g(x)`

∴
`f(x) = (1)/(3) ^(2 \cdot x)` ≡
`g(x) = 9^(-x)`

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

`f(x) = (1)/(3) ^(2 \cdot x) = \left ((1)/(3) ^2\right )^x = \left ((1)/(9) \right )^x = g(x)`

∴
`f(x) = (1)/(3) ^(2 \cdot x)` ≡
`g(x) = \left ((1)/(9) \right )^x`