Respuesta :

frika

Given the function [tex]f(x)=-2\cdot 3^{1-x}.[/tex]

1. Note that [tex]3^{1-x}=3^1\cdot 3^{-x}=3\cdot \dfrac{1}{3^x}=3\cdot \left(\dfrac{1}{3}\right)^x.[/tex]

2. Substitute previous expression into the function:

[tex]f(x)=-2\cdot 3^{1-x}=-2\cdot 3\cdot \left(\dfrac{1}{3}\right)^x=-6\cdot \left(\dfrac{1}{3}\right)^x .[/tex]

Answer: correct choice is D

alinakincsem

Answer:

The correct answer option is D. [tex]f(x) = -6.(\frac{1}{3} )^x[/tex]

Step-by-step explanation:.

We are given a function [tex]f(x) = -2.3^{(1-x)}[/tex] and we are supposed to convert it to the form [tex]f(x) = ab^x[/tex].

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

-2 = -2

while [tex]3^{(1-x)}[/tex] can be written as:

[tex]3^1.3^{-x}[/tex] = [tex]3^1.\frac{1}{3^x} = 3.(\frac{1}{3} )^x[/tex]

Combining these two terms to get:

[tex]-2.3.(\frac{1}{3} )^x[/tex]

[tex]-6.(\frac{1}{3} )^x[/tex]

Therefore, the given function in the form [tex]f(x) = ab^x[/tex] is [tex]f(x) = -6.(\frac{1}{3} )^x[/tex].

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