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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]

Annual interest rate is 4.6%

hope this helps!

Answer:

744

Step-by-step explanation:

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:

The fourth one

Step-by-step explanation:

I know that is correct

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:

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]

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

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:

30

Step-by-step explanation:

Answer:

the answer is defently 405

Step-by-step explanation:

so you have 400 and 5 and 400+5=405

Answer:

a is possible

b is not possible

c is possible

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

Step-by-step explanation:

Answer:

$6.75

Step-by-step explanation:

Divide 33.75 by 5, they are $6.75 each

Answer: 4

Step-by-step explanation:

 Slope = -2.000/2.000 = -1.000

 x-intercept = 0/1 = 0.00000

 f-intercept = 0/1 = 0.00000

x = 0

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:

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:

B

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

Answer:

A and D

Step-by-step explanation:

[tex]20 r + 60t = 20(r+3t) = 4\cdot 5(r +3t)=4(5r +15t)[/tex]

[tex](b) ^{2} + {(h)}^{2} = {(x)}^{2} \: \: \: ( by \: \: \: pythagoras \: \: \: theorem)\\ = > {(10)}^{2} + {(10)}^{2} = {(x)}^{2} \\ = > 100 + 100 = {x}^{2} \\ = > 200 = {x}^{2} \\ = > x = \sqrt{200} mm \\ = > x = \sqrt{2 \times 2 \times 2 \times 5 \times 5}mm \\ = > x = 2 \times 5 \sqrt{2} mm \\ = > x = 10 \sqrt{2} mm[/tex]

Answer:

10√2 mm.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

6/7

Step-by-step explanation:

Answer:

24%

Step-by-step explanation:

consider bag 1: there are 3 vowel tiles (out of 5) in this bag so the probability of choosing a vowel tile would be 3/5

bag 2: there are 2 vowel tiles (out of 5) in this bag so the probability of choosing a vowel tile would be 2/5

to find the probability of getting two vowel tiles (one from each bag), you multiply these two probabilities together:

3/5 *2/5 to get 6/25 which is equal to 0.24 or 24%

Answer:

0.3

Step-by-step explanation:

hopes this helps

Answer:

20%

Step-by-step explanation:

54-45 = 9

9/45 = 0.2

0.2*100 = 20

Production increased 20%

Answer:

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

Step-by-step explanation:

Im not 100% sure about c and d

Answer:

$31.95 Before tip.

Step-by-step explanation:

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