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Rzqust [24]
3 years ago
5

Find the inverse of the function. f(x) = 6x3 - 8

Mathematics
2 answers:
mr Goodwill [35]3 years ago
8 0
Replace <span><span>f<span>(x)</span></span><span>fx</span></span> with <span>yy</span>.<span><span>y=<span><span>6<span>x3</span></span><span>−8</span></span></span><span>y=<span><span>6<span>x3</span></span><span>-8</span></span></span></span>Interchange the variables.<span><span>x=<span><span>6<span>y3</span></span><span>−8</span></span></span><span>x=<span><span>6<span>y3</span></span><span>-8</span></span></span></span>Solve for <span>yy</span>.
<span><span>y=<span><span>3<span>√<span>36<span>(<span>x+8</span>)</span></span></span></span>6</span></span><span>y=<span><span><span>36<span>x+8</span></span>3</span>6</span></span></span>Solve for <span>yy</span> and replace with <span><span><span>f<span>−1</span></span><span>(x)</span></span><span><span>f<span>-1</span></span>x</span></span>.
<span><span><span>f<span>−1</span></span><span>(x)</span></span>=<span><span>3<span>√<span>36<span>(<span>x+8</span>)</span></span></span></span><span>6</span></span></span>
Softa [21]3 years ago
6 0

Answer:

f^{-1}(x) = \sqrt[3]{\frac{x+8}{6}}

Step-by-step explanation:

Given function,

f(x)=6x^3-8

Replace f(x) by y,

y=6x^3-8

Switch x and y,

x=6y^3-8

Isolate y in the left side,

-6y^3=-x-8

6y^3=x+8

y^3=\frac{x+8}{6}

y=\sqrt[3]{\frac{x+8}{6}}

Replace y by f^{-1}(x)

\implies f^{-1}(x) = \sqrt[3]{\frac{x+8}{6}}

Which is the required inverse of the given function.

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Calculate the expected value, the variance, and the standard deviation of the given random variable X. (Round all answers to two
Tom [10]

Answer:

E (X) = 1.8

Var (X) = 0.36

σ = 0.6

Step-by-step explanation:

Solution:-

- Denote the random variable X : is the number of red marbles that Suzan has in her hand after she selects three marbles.

- Total sample space (bag) have the following quantity of colored marbles:

                Bag : { 3 Red , 2 Green }

- Suzan selects three marbles from the bag. The Event (X) defines the number of red marbles out of 3.

- The total number of outcomes / selections for randomly selecting 3 balls from the bag:

               All outcomes = 5 C 3 = 10

- The probability distribution of the random variable X, we will use combinations to determine the required probabilities:

  X = 1 red marble:

        P ( X = 1 ) : Suzan chooses 1 Red marble from the available 3 red marble and 2 green marbles.

        P ( X = 1 ) = [ 3C1*2C2 ] / all outcomes = (3*1) / 10 = 0.3

X = 2 red marble:

        P ( X = 2 ) : Suzan chooses 2 Red marble from the available 3 red marble and 1 green marbles.

        P ( X = 2 ) = [ 3C2*2C1 ] / all outcomes = (3*2) / 10 = 0.6

X = 3 red marble:

        P ( X = 3 ) : Suzan chooses 3 Red marble from the available 3 red marble.

        P ( X = 3 ) = [ 3C3] / all outcomes = (1) / 10 = 0.1

- The probability distribution is as follows:

          X :         1                 2                3

       P (X):       0.3            0.6              0.1

- The expected value E(X) for the given random variable X is:

                E ( X ) = ∑Xi*P(Xi)

                           = 1*0.3 + 2*0.6 + 3*0.1

                           =1.8

- The variance Var(X) for the given random variable X is:

                Var ( X ) = ∑Xi^2*P(Xi) - [ E(X) ] ^2

                               = 1^2*0.3 + 2^2*0.6 + 3^2*0.1 - 1.8^2

                               = 0.36

- The standard deviation for the given random variable X is:

                σ = √Var(X)

                σ = √0.36

                σ = 0.6

5 0
3 years ago
What is the solution of x-7= ir+14,
weqwewe [10]

Answer:

x=12

Step-by-step explanation:

put the x at one side and the numbers ar the other

5/2x-3/4x=14+7

10/4x-3/4x=21

7/4x=21

7x=84

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Please help with part A!!
zaharov [31]

Answer:

Option A. A and D

Step-by-step explanation:

This answer because they are both right triangles and are near the same size

Hope this helps!

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3 years ago
2 × 7/8 as a model how do I draw it as a model
White raven [17]
One way to do it is you can draw two sets of 7/8.


You can draw 8 tiles, and color in 7.

Draw that two times.

That’s one way, but that might not be the way you learned it.


Hope this helped anyways!
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Carpeting costs $9.95 per yard. If Jamie buys 8 yards, how much will it cost him?
Hatshy [7]

Answer:

$79.6

Step-by-step explanation:

9.95 x 8 = 79.6

8 0
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