Question

PLS HELP

Simplify the function f(x) =
3x
(81)
4
Then determine the key aspects of the function.
The initial value is
The simplified base is
The domain is
The range is

Answer 1

Explanation:

This follows the form

`y=a(b)^x`

where a is the initial value and b is the base with the exponent. Using that information, we can see that the initial value in our function is 1/3. Simplifying the base will take some work. Let's first rewrite this is a radical:

`81^{(3x)/(4) }=\sqrt[4]{81^(3x) }`

Now let's break up 81 into its factors. 81 is 9*9 which is 3*3*3*3. Therefore,

`81=3^4`

We will use that as a simplification:

`\sqrt[4]{(3^4)^(3x)}` which simplifies to

`\sqrt[4]{3^(12x)}`

Rewriting that as an exponent looks like this:

`3^{(12x)/(4)}` which simplifies to

`3^(3x)`

That's the answer for the second part. The whole exponential equation now is

`f(x)=(1)/(3)(3)^(3x)`

The domain for an exponential function is all real numbers and the range is

y > 0

Answer 2

1/3

27

all real numbers

y > 0

ON EDGE

Explanation: