Question

Write the exponential function f(x)= -2*3^(1-x)

Answer 1

The correct answer option is D.
`f(x) = -6.((1)/(3) )^x`

Step-by-step explanation:.

We are given a function
`f(x) = -2.3^((1-x))` and we are supposed to convert it to the form
`f(x) = ab^x`.

For this, we will break the given function to make it easier to solve.

-2 = -2

while
`3^((1-x))` can be written as:

`3^1.3^(-x)` =
`3^1.(1)/(3^x) = 3.((1)/(3) )^x`

Combining these two terms to get:

`-2.3.((1)/(3) )^x`

`-6.((1)/(3) )^x`

Therefore, the given function in the form
`f(x) = ab^x` is
`f(x) = -6.((1)/(3) )^x`.

Answer 2

Given the function
`f(x)=-2\cdot 3^(1-x).`

1. Note that
`3^(1-x)=3^1\cdot 3^(-x)=3\cdot (1)/(3^x)=3\cdot \left((1)/(3)\right)^x.`

2. Substitute previous expression into the function:

`f(x)=-2\cdot 3^(1-x)=-2\cdot 3\cdot \left((1)/(3)\right)^x=-6\cdot \left((1)/(3)\right)^x .`

Answer: correct choice is D