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g(x) as given has no inverse because there are instances of two x values giving the same value of g(x). For instance,

x = -1   ⇒   g(-1) = 4 (-1 + 3)² - 8 = 8

x = -5   ⇒   g(-5) = 4 (-5 + 3)² - 8 = 8

Only a one-to-one function can have an inverse. g(x) is not one-to-one.

However, if we restrict the domain of g(x), we can find an inverse over that domain. Let [tex]g^{-1}(x)[/tex] be the inverse of g(x). Then by definition of inverse function,

[tex]g\left(g^{-1}(x)\right) = 4 \left(g^{-1}(x) + 3\right)^2 - 8 = x[/tex]

Solve for the inverse:

[tex]4 \left(g^{-1}(x) + 3\right)^2 - 8 = x[/tex]

[tex]4 \left(g^{-1}(x) + 3\right)^2 = x + 8[/tex]

[tex]\left(g^{-1}(x) + 3\right)^2 = \dfrac{x + 8}4[/tex]

[tex]\sqrt{\left(g^{-1}(x) + 3\right)^2} = \sqrt{\dfrac{x + 8}4}[/tex]

[tex]\left| g^{-1}(x) + 3 \right| = \dfrac{\sqrt{x+8}}2[/tex]

Recall the definition of absolute value:

[tex]|x| = \begin{cases}x & \text{if }x\ge0\\-x&\text{if }x<0\end{cases}[/tex]

This means there are two possible solutions for the inverse of g(x) :

• if [tex]g^{-1}(x) + 3 \ge 0[/tex], then

[tex]g^{-1}(x) + 3 = \dfrac{\sqrt{x+8}}2 \implies g^{-1}(x) = -3+\dfrac{\sqrt{x+8}}2[/tex]

• otherwise, if [tex]g^{-1}(x)+3<0[/tex], then

[tex]-\left(g^{-1}(x) + 3\right) = \dfrac{\sqrt{x+8}}2 \implies g^{-1}(x) = -3-\dfrac{\sqrt{x+8}}2[/tex]

Which we choose as the inverse depends on how we restrict the domain of g(x). For example:

Remember that the inverse must satisfy

[tex]g\left(g^{-1}(x)\right) = x[/tex]

In the first case above, [tex]g^{-1}(x) + 3 \ge 0[/tex], or [tex]g^{-1}(x) \ge -3[/tex]. This suggests that we could restrict the domain of g(x) to be [tex]x \ge -3[/tex].

Then as long as [tex]x \ge -3[/tex], the inverse is

[tex]g^{-1}(x) = -3+\dfrac{\sqrt{x+8}}2[/tex]

Answer:

0.3

Step-by-step explanation:

hopes this helps

Step-by-step explanation:

4(x-3)-8=16

4x-12-8=16

4x-20=16

4x-20+20=16+20

add

4x=36

divide both

4x/4  36/4

Simplify

x = 9

Answer:

68 degrees fahrenheit.

Step-by-step explanation:

Formula:

(20°C × 9/5) + 32 = 68°F

Answer:

Its around 68F

Step-by-step explanation:

Hope this helped

Answer:

a is possible

b is not possible

c is possible

Answer:

B

Step-by-step explanation: Because he gains $25, which is positive

Answer:

$31.95 Before tip.

Step-by-step explanation:

I believe you should just add 17.75+80%=31.95

Using the binomial distribution, it is found that there is a 0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.

For each free throw, there are only two possible outcomes, either he makes it, or he misses it. The results of free throws are independent from each other, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that he makes exactly 1 is P(X = 1), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{3,1}.(0.9)^{1}.(0.1)^{2} = 0.027[/tex]

0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.

To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377

Answer:

0.03

Step-by-step explanation:

I just did it on Khan

Answer: i got you my boi answer is x > -3

Step-by-step explanation:

Answer:

6/7

Step-by-step explanation:

Answer:

area = PI x r^2

area = 3.14 x 13^2

area = 3.14 x 169

area = 530.66

Step-by-step explanation:

Plz Mark as brainliest hope this helps

Answer:

30

Step-by-step explanation:

Answer:

See attachment

Step-by-step explanation:

Answer:

1st - Matthew

2nd - Kiera

3rd - Jeffrey

4th - Austin

5th - Shelby

The sequence of the statement will be Matthew is in the first place, Kiera is in second place, Jeffrey is in third place, Austin is in fourth place, and Shelby is in fifth place.

An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.

Given:

Austin didn’t win first or last place,

The snowmen wearing scarves with stripes were in second and last place,

Austin’s snowman came in after Jeffrey’s but before Shelby’s snowman,

Keira placed better than Shelby, but not as well as Matthew,

The sequence of the above statement can be written as,

1st - Matthew

2nd - Kiera

3rd - Jeffrey

4th - Austin

5th - Shelby

To know more about the sequence:

https://brainly.com/question/28615767

#SPJ2

Annual interest rate is 4.6%

hope this helps!

Answer:

37

Step-by-step explanation:

All angles of a triangle have to add up to 180 degrees

180 - 113 - 30 = 37

37+113+30 = 180

Answer:

2 Packages

Step-by-step explanation:

To last the whole month, we would need to multiply 1/4 by 8.

1 *8 = 8

4 * 1 = 4

8/4 = 2

Using proportions, it is found that Ankita's share is of [tex]\frac{x}{4}[/tex], considering that the total rent is of x Rp.r.

The rule of three is:

4 people - x

1 people - a

Applying cross multiplication:

[tex]4a = x[/tex]

[tex]a = \frac{x}{4}[/tex]

Ankita's share is of [tex]\frac{x}{4}[/tex], considering that the total rent is of x Rp.r.

You can learn more about proportions at https://brainly.com/question/24372153

Answer:

a) -inf b) DNE c) 2 d) 3 e) 1

Step-by-step explanation:

Im not 100% sure about c and d

The area of the composite figuren as shown in the diagram is 90 in².

Area is the region bounded by a plane shape.

To calculate the area of the figure, we use the formula below

Formula:

Where:

Substitute these values into equation 1

Learn more about area here: https://brainly.com/question/28470545

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Answer:

45 is 150% of 30.

Step-by-step explanation:

To find what percent of 30 is 45 first we must turn it into a fraction and simplify.

fraction form: 45/30

simplified fraction form: 3/2

now to find percent you have to put a number over one hundred.

3/2 = ?/100

Right now our denominator is 2. By what number can we multiply 2 to get to 100? The answer is 50.

Now that we have multiplied the denominator by 50, we also have to multiply the numerator (3) by fifty. 3 x 50 = 150

so now we put the new numerator and denominator together and get 150/100

The answer is 150%

Answer:

-4 -2 1 the top are 2/6 -2/8

Step-by-step explanation:

I don't know if that's right but yea hope that helps

Answer:

The fourth one

Step-by-step explanation:

I know that is correct

Answer is attached.

Hope it helps :)

Answer:

20%

Step-by-step explanation:

54-45 = 9

9/45 = 0.2

0.2*100 = 20

Production increased 20%

Answer:

10z + 5    

Step-by-step explanation:

(3 z + 1) + (5 + 7 z )

3 z + 1 + 5 + 7 z     [Remove parentheses]

10z + 5                 [Combine like terms]

.

[tex]10z + 6[/tex]

[tex]3z + 7z + 5 + 1 = 10z + 6[/tex]

Answer:

3sqrt(2)

Step-by-step explanation:

72=6^2 x 2 so sqrt(72)=6sqrt(2)

divide by 2 to get 3sqrt(2)

Answer:

[tex]answer \: is \: = \: \sqrt[6]{2} [/tex]

[tex]to \: know \: the \: answer \: with \: proof[/tex]

[tex]refer \: to \: the \: above \: attatchmet \: [/tex]