Answer:
the answer is your welcome
$33.52
For a given function f(x) we define the domain restrictions as values of x that we can not use in our function. Also, for a function f(x) we define the inverse g(x) as a function such that:
g(f(x)) = x = f(g(x))
<u>The restriction is:</u>
x ≠ 4
<u>The inverse is:</u>
![y = 4 + \sqrt{\frac{11}{x} }](https://tex.z-dn.net/?f=y%20%3D%204%20%2B%20%5Csqrt%7B%5Cfrac%7B11%7D%7Bx%7D%20%7D)
Here our function is:
![f(x) = \frac{11}{(x - 4)^2}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B11%7D%7B%28x%20-%204%29%5E2%7D)
We know that we can not divide by zero, so the only restriction in this function will be the one that makes the denominator equal to zero.
(x - 4)^2 = 0
x - 4 = 0
x = 4
So the only value of x that we need to remove from the domain is x = 4.
To find the inverse we try with the general form:
![g(x) = a + \sqrt{\frac{b}{x} }](https://tex.z-dn.net/?f=g%28x%29%20%3D%20a%20%2B%20%5Csqrt%7B%5Cfrac%7Bb%7D%7Bx%7D%20%7D)
Evaluating this in our function we get:
![g(f(x)) = a + \sqrt{\frac{b}{f(x)} } = a + \sqrt{\frac{b*(x - 4)^2}{11 }}\\\\g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4)](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%20a%20%2B%20%5Csqrt%7B%5Cfrac%7Bb%7D%7Bf%28x%29%7D%20%7D%20%20%3D%20a%20%2B%20%5Csqrt%7B%5Cfrac%7Bb%2A%28x%20-%204%29%5E2%7D%7B11%20%7D%7D%5C%5C%5C%5Cg%28f%28x%29%29%20%3D%20a%20%2B%20%5Csqrt%7B%5Cfrac%7Bb%7D%7B11%20%7D%7D%2A%28x%20-%204%29)
Remember that the thing above must be equal to x, so we get:
![g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4) = x\\\\{\frac{b}{11 }} = 1\\{\frac{b}{11 }}*4 - a = 0](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%20a%20%2B%20%5Csqrt%7B%5Cfrac%7Bb%7D%7B11%20%7D%7D%2A%28x%20-%204%29%20%3D%20x%5C%5C%5C%5C%7B%5Cfrac%7Bb%7D%7B11%20%7D%7D%20%3D%201%5C%5C%7B%5Cfrac%7Bb%7D%7B11%20%7D%7D%2A4%20-%20a%20%3D%200)
From the two above equations we find:
b = 11
a = 4
Thus the inverse equation is:
![y = 4 + \sqrt{\frac{11}{x} }](https://tex.z-dn.net/?f=y%20%3D%204%20%2B%20%5Csqrt%7B%5Cfrac%7B11%7D%7Bx%7D%20%7D)
If you want to learn more, you can read:
brainly.com/question/10300045
Answer:
probability that an athlete who tests positive is actually a user
= 0.2177
Step-by-step explanation:
To solve this problem, we create a table that relates the test results and the status of the athletes.
We arbitrarily take a sample of 10000 atheletes to work with whole numbers.
Out of that, 300 are users (3% on the average), and 9700 are non users.
Of the users, 270 users will test positive (90% accuracy) and 30 will test negative.
Similarly, of the non-users, 970 will test positive, and 8730 will test negative.
This gives 1240 positive tests, and 8760 negative tests.
Of the 1240 who test positive, 270 are actually users.
Therefore the probability of the positive test results are actually users
= 270/1240 = 0.2177
Answer:
Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:
Step-by-step explanation:
Given the point (-5, 5)
slope = m = -8/5
Using the slope intercept form:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Plugging point (-5, 5) and slope = m = -8/5 in the slope intercept form to find the y-intercept 'b'.
![5=\frac{-8}{5}\left(-5\right)+b](https://tex.z-dn.net/?f=5%3D%5Cfrac%7B-8%7D%7B5%7D%5Cleft%28-5%5Cright%29%2Bb)
![\mathrm{Switch\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BSwitch%5C%3Asides%7D)
![\frac{-8}{5}\left(-5\right)+b=5](https://tex.z-dn.net/?f=%5Cfrac%7B-8%7D%7B5%7D%5Cleft%28-5%5Cright%29%2Bb%3D5)
![8+b=5](https://tex.z-dn.net/?f=8%2Bb%3D5)
![8+b-8=5-8](https://tex.z-dn.net/?f=8%2Bb-8%3D5-8)
![b=-3](https://tex.z-dn.net/?f=b%3D-3)
so the equation of the line will be:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
plugging m = -8/5 and b = -3 in slope intercept form
Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:
Answer:
0
Step-by-step explanation: