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pantera1 [17]
3 years ago
8

MAX POINTS TO BEST ANSWER!

Mathematics
1 answer:
NISA [10]3 years ago
5 0

Note: (f/g)(x) can be written as

f(x)/g(x). This simply means f(x) divided by g(x).

We know what f(x) and g(x) are because that information is given to us in the problem. See it?

Set up the rational function and factor.

(x^2 - 9)/(x^2 -4x + 3)

We now factor the top and bottom.

(x - 3)(x + 3)/(x - 3)(x - 1)

Cancel out common terms.

We now have (x + 3)/(x - 1) as the reduced rational function.

To find the domain, set the bottom to 0 and solve for x.

x - 1 = 0

x = 1

The domain is ALL REAL NUMBERS EXCEPT FOR 1. In the given function, x CANNOT BE 3 because this would create a zero in the denominator.

Answer in interval notation is

(-00, 1) U (1, 3) U (1, 00).

The interval notation reads as follows:

All negative numbers included but not 1 united with the open interval that does not include 1 and 3 united with the interval that excludes 1 but includes all positive numbers greater than 1. I hope this is clear.

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wariber [46]

Answer:

k=2

Step-by-step explanation:

3^k*2 * 3^-k+2 = 81

Factor out 81 to be : 3^4

Rewrite the equation:

k*2 - k+2 = 4

k^2 - 2k = 4

Simplify : k+2 = 4

            <u>    - 2   - 2</u>

             k = 2

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20 POINTS + BRAINLIEST! NEED HELP FAST!
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shutvik [7]
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Find each product.
kvasek [131]

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3 years ago
a. Rewrite the equation in exponential form.b. Create a table of coordinates, using the exponential form from part (a). Begin by
Bond [772]

Gven

The lograthmic function, lograthmic fu

y=\log_4x

To find:

a) Rewrite the function in exponential form.

b) For each given value of y, find the value of x to complete the ordered pair.

c) The graph of the function.

Explanation:

It is given that,

y=\log_4x

a) Since,

It is known that,

\begin{gathered} y=\log_ax \\ \Rightarrow x=a^y \end{gathered}

Then,

x=4^y

Hence, the exponential form of the function is,

x=4^y

b) Also,

For y = -2,.

The value of x is given by,

\begin{gathered}  \\ \Rightarrow x=4^{-2} \\ \Rightarrow x=\frac{1}{4^2} \\ \Rightarrow x=\frac{1}{16} \end{gathered}

Hence, the ordered pair is (1/16, -2).

For y = -1,

\begin{gathered} x=4^{-1} \\ x=\frac{1}{4} \end{gathered}

Hence, the ordered pair is (1/4, -1).

For y = 0,

\begin{gathered} x=4^0 \\ x=1 \end{gathered}

Hence, the ordered pair is (1, 0).

For y = 1,

\begin{gathered} x=4^1 \\ x=4 \end{gathered}

Hence, the ordered pair is (4, 1).

For y = 2,

\begin{gathered} x=4^2 \\ x=16 \end{gathered}

Hence, the ordered pair is (16, 2).

c) Also, the graph of the given function is,

7 0
1 year ago
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