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Luda [366]
3 years ago
9

Provide an example of a function that does not have an inverse function. How do you prove that it is not a function?

Mathematics
1 answer:
slavikrds [6]3 years ago
5 0

If f had an inverse, then its graph would be the reflection of the graph of f about the line y = x. The graph of f and its reflection about y = x are drawn below. Note that the reflected graph does not pass the vertical line test, so it is not the graph of a function.

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Jacques needs to convert the function f(x) = x2 − 6x + 14 to vertex form, f(x) = (x − h)2 + k, in order to find the minimum.
Anarel [89]

k = 5

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

Since the coefficient of the x² term is 1 then

add/ subtract (half the coefficient of the x-term )² to x² - 6x

f(x) = x² + 2(- 3)x + 9 - 9 + 14 = (x - 3)² + 5 → k = 5


   

5 0
3 years ago
Read 2 more answers
Alonzo and miguel scored a total of 40 points in the basketball game.miguel scored four more points than twice alonzo's score .H
elena-14-01-66 [18.8K]
I can tell you that you have to multiply Alonzo score by 16
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8 0
3 years ago
A researcher claims that the variation in the salaries of elementary school teachers is greater than the variation in the salari
guajiro [1.7K]

Answer:

a

The null hypothesis is  H_o :  \sigma^2_1 = \sigma^2 _2

The alternative hypothesis is H_a :  \sigma_1 ^2 > \sigma^2_2

b

F_{critical} = 1.8608

c

F = 2.9085

d

    The decision rule is  

Reject the null hypothesis

e

There is sufficient evidence to support the researchers claim

Step-by-step explanation:

From the question we are told that

 The first sample size is  n_1 = 30

 The sample variance for elementary school is  s^2_1 = 8324

 The second sample size is  n_2 = 30

  The sample variance for the secondary school is  s^2_2 = 2862

   The significance level is  \alpha = 0.05

The null hypothesis is  H_o :  \sigma^2_1 = \sigma^2 _2

The alternative hypothesis is H_a :  \sigma_1 ^2 > \sigma^2_2

Generally from the F statistics table  the critical value of \alpha = 0.05 at first and  second degree of freedom df_1 = n_1 - 1 = 30 - 1 = 29 and  df_2 = n_2 - 1 = 30 - 1 = 29 is  

         F_{critical} = 1.8608

Generally the test statistics is mathematically represented as

       F = \frac{s_1^2 }{s_2^2}

=>   F = \frac{8324 }{2862}

=>   F = 2.9085

Generally from the value obtained we see that  F >  F_{critical } Hence

   The decision rule is  

Reject the null hypothesis

    The conclusion is  

  There is sufficient evidence to support the researchers claim

   

4 0
2 years ago
If there are 23 students in your class, and your teacher is pulling random names from a hat, what is the probability that your n
krok68 [10]

If the teacher isn't putting the names back in the hat then it would be 1/21 if she is then 1/23

3 0
2 years ago
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Confidence Interval Application Many people feel that the drying of pavement marking paint is much too slow. You spend several d
djyliett [7]

Answer:

The sample size is  n =33

Step-by-step explanation:

From the question we are told that

  The margin of error is E  =  1.5 seconds

   The standard deviation is  s =  4 seconds

 Given that the confidence level is 97% then the level of significance is mathematically represented as

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=>   \alpha  =  0.03

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  2.17

Generally the sample size is mathematically represented as

    n  =[  \frac{Z_{\frac{\sigma }{2 } } *  \sigma }{E} ]^2

=> n  =[  \frac{2.17  * 4 }{1.5} ]^2

=>  n =33

7 0
3 years ago
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