The domain and range of a function are the possible <em>x and y values </em>of the function.
<em>The domain and the range of the function is: (a) </em>
<em> and </em>
<em />
The functions are given as:
![\mathbf{f(x) = \frac{4}{x^2 - 4}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%20%5Cfrac%7B4%7D%7Bx%5E2%20-%204%7D%7D)
![\mathbf{g(x) = x + 2}](https://tex.z-dn.net/?f=%5Cmathbf%7Bg%28x%29%20%3D%20x%20%2B%202%7D)
(g o f)(x) is calculated as:
![\mathbf{(g\ o\ f)(x) = g(f(x))}](https://tex.z-dn.net/?f=%5Cmathbf%7B%28g%5C%20o%5C%20f%29%28x%29%20%3D%20g%28f%28x%29%29%7D)
So, we have:
![\mathbf{(g\ o\ f)(x) = \frac{4}{x^2 - 4} + 2}](https://tex.z-dn.net/?f=%5Cmathbf%7B%28g%5C%20o%5C%20f%29%28x%29%20%3D%20%5Cfrac%7B4%7D%7Bx%5E2%20-%204%7D%20%2B%202%7D)
Take LCM
![\mathbf{(g\ o\ f)(x) = \frac{4 + 2x^2 - 8}{x^2 - 4} }](https://tex.z-dn.net/?f=%5Cmathbf%7B%28g%5C%20o%5C%20f%29%28x%29%20%3D%20%5Cfrac%7B4%20%2B%202x%5E2%20-%208%7D%7Bx%5E2%20-%204%7D%20%7D)
![\mathbf{(g\ o\ f)(x) = \frac{2x^2 - 4}{x^2 - 4} }](https://tex.z-dn.net/?f=%5Cmathbf%7B%28g%5C%20o%5C%20f%29%28x%29%20%3D%20%5Cfrac%7B2x%5E2%20-%204%7D%7Bx%5E2%20-%204%7D%20%7D)
Represent the denominator as follows, to calculate the domain
![\mathbf{x^2 - 4 \ne 0 }](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%5E2%20-%204%20%5Cne%200%20%7D)
Add 4 to both sides
![\mathbf{x^2 \ne 4 }](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%5E2%20%5Cne%204%20%7D)
Take square roots of bot sides
![\mathbf{x \ne \±2 }](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%20%5Cne%20%5C%C2%B12%20%7D)
Hence, the domain of the function is:
![\mathbf{D:\{x \in R|x \ne -2,2\}}](https://tex.z-dn.net/?f=%5Cmathbf%7BD%3A%5C%7Bx%20%5Cin%20R%7Cx%20%5Cne%20-2%2C2%5C%7D%7D)
On the graph of
(see attachment), the function does not have a value from <em>y = 1 to 2.</em>
Hence, the range is:
![\mathbf{R:\{(-\infty,1) \cup (2,\infty)\}}](https://tex.z-dn.net/?f=%5Cmathbf%7BR%3A%5C%7B%28-%5Cinfty%2C1%29%20%5Ccup%20%282%2C%5Cinfty%29%5C%7D%7D)
Read more about domain and range at:
brainly.com/question/1632425
Answer:
4.32 = k
Step-by-step explanation:
8/k = 5/2.7
We can solve using cross products
8* 2.7 = 5k
21.6 = 5k
Divide each side by 5
21.6/5 = k
4.32 = k
25% is the percentage of magazines
Answer:
57 4/5
Step-by-step explanation:
Add 5 and 14
5+14 = 19
Triple the sum
3 * 19 = 57
The add 4/5
57 + 4/5
57 4/5
6/y=9/5(due to similarity)
y=6*5/9=30/9=10/3=3.333..