Question

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

Answer 1

Answer:

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

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:

$3^1.3^{-x}$ = $3^1.\frac{1}{3^x} = 3.(\frac{1}{3} )^x$

Combining these two terms to get:

$-2.3.(\frac{1}{3} )^x$

$-6.(\frac{1}{3} )^x$

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

Answer 2

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

1. Note that $3^{1-x}=3^1\cdot 3^{-x}=3\cdot \dfrac{1}{3^x}=3\cdot \left(\dfrac{1}{3}\right)^x.$

2. Substitute previous expression into the function:

$f(x)=-2\cdot 3^{1-x}=-2\cdot 3\cdot \left(\dfrac{1}{3}\right)^x=-6\cdot \left(\dfrac{1}{3}\right)^x .$

Answer: correct choice is D