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REY [17]
3 years ago
13

For the function f(x) = x2 ­ -12, find (f o f­-1)(4) A. 0 B. 4 C. 10 D. 6

Mathematics
1 answer:
slega [8]3 years ago
5 0

We actually don't need to do any computation. By definition, the inverse function f^{-1} changes the role of input and output. So, if a function f maps x onto y, the inverse function maps y onto x.

You have to think like this: if the function makes a step further, the inverse function makes that same step back.

This means that the composition f \circ f^{-1} is always the identity function f(x) = x. In fact,

(f\circ f^{-1})(x) = f(f^{-1}(x)) = x

So, for every function, you have

(f\circ f^{-1})(4) = f(f^{-1}(4)) = 4

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guajiro [1.7K]

Answer:

198

Step-by-step explanation:

7 0
3 years ago
Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 16 hav
Furkat [3]

Answer:

  • There is no significant evidence that p1 is different than p2 at 0.01 significance level.
  • 99% confidence interval for p1-p2 is  -0.171 ±0.237 that is (−0.408, 0.066)

Step-by-step explanation:

Let p1 be the proportion of the common attribute in population1

And p2 be the proportion of the same common attribute in population2

H_{0}: p1-p2=0

H_{a}: p1-p2≠0

Test statistic can be found using the equation:

z=\frac{p2-p1}{\sqrt{{p*(1-p)*(\frac{1}{n1} +\frac{1}{n2}) }}} where

  • p1 is the sample proportion of the common attribute in population1 (\frac{16}{30} =0.533)
  • p2 is the sample proportion of the common attribute in population2 (\frac{1337}{1900} =0.704)
  • p is the pool proportion of p1 and p2 (\frac{16+1337}{30+1900}=0.701)
  • n1 is the sample size of the people from population1 (30)
  • n2 is the sample size of the people from population2 (1900)

Then z=\frac{0.704-0.533}{\sqrt{{0.701*0.299*(\frac{1}{30} +\frac{1}{1900}) }}} ≈ 2.03

p-value of the test statistic is  0.042>0.01, therefore we fail to reject the null hypothesis. There is no significant evidence that p1 is different than p2.

99% confidence interval estimate for p1-p2 can be calculated using the equation

p1-p2±z*\sqrt{\frac{p1*(1-p1)}{n1}+\frac{p2*(1-p2)}{n2}} where

  • z is the z-statistic for the 99% confidence (2.58)

Thus 99% confidence interval is

0.533-0.704±2.58*\sqrt{\frac{0.533*0.467}{30}+\frac{0.704*0.296}{1900}} ≈ -0.171 ±0.237 that is (−0.408, 0.066)

7 0
3 years ago
Which symbol correctly compares the fractions below?<br> 1/8 ? 1/2
antoniya [11.8K]

Answer:

<

Step-by-step explanation:

1/2 = 4/8

=> 1/8 < 4/8

=> 1/8 < 1/2

6 0
3 years ago
Marcy bought 10.32 pounds of white potatoes and 12.48 pounds of sweet potatoes. About how many pounds of potatoes did Marcy buy?
zalisa [80]
Marcy bought a total of 22.8 potatoes. 10.32+12.48=22.8
3 0
3 years ago
Brainliest to who answers first!
alexdok [17]

Answer:

correct answers

15 m=1,500

117 mm=0.117 m

79 m=0.079 km

hope it helps

5 0
3 years ago
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