One granola bar and one bottle of water will cost 3 dollars.
This is because both a granola bar and bottle of water cost $1.50
You can get 8 half-cups of trail mix. All you have to do is 4*2
Answer:all real numbers except 4 and 2
Explanation:The given function is:
f(x) =
![\frac{x+1}{x^2-6x+8}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%2B1%7D%7Bx%5E2-6x%2B8%7D%20)
Domain of the function is defined as the values of x that can be used to substitute in the function.
We know that any fraction cannot have a zero in its denominator. Because if this happens, then the fraction would be undefined.
This means that in the given function, we cannot substitute with any value for x that makes the denominator a zero.
Now, we will get the zeroes of the denominator as follows:
x² - 6x + 8 = 0
(x-4)(x-2) = 0
either x-4 = 0 ...........> x = 4
or x-2 = 0 .............> x = 2
Based on the above, we can substitute with any value for x excluding 4 and 2.
This means that the domain of the function is any real real number except 4 and 2
Hope this helps :)
Answer:
The inner function is
.
The outer function is
.
![\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20y%5E%7B%5Cprime%7D%20%3D%20%5Csec%5E%7B2%7D%28u%29%2A%5Cpi%20%3D%20%5Cpi%5Csec%5E%7B2%7D%7B%5Cpi%20x%7D)
Step-by-step explanation:
The inner function is the one we apply the outer function to.
So
![y = \tan{\pi x}](https://tex.z-dn.net/?f=y%20%3D%20%5Ctan%7B%5Cpi%20x%7D)
We apply the outer function tangent to
.
So, the inner function is
.
The outer function is
.
The derivative of a compositve function
in which
is given by the following function.
![y^{\prime} = f^{\prime}(u)*g^{\prime}(x)](https://tex.z-dn.net/?f=y%5E%7B%5Cprime%7D%20%3D%20f%5E%7B%5Cprime%7D%28u%29%2Ag%5E%7B%5Cprime%7D%28x%29)
So
![f(u) = \tan{u}](https://tex.z-dn.net/?f=f%28u%29%20%3D%20%5Ctan%7Bu%7D)
![f^{\prime}(u) = \sec^{2}{u}](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28u%29%20%3D%20%5Csec%5E%7B2%7D%7Bu%7D)
![u = g(x) = \pi x](https://tex.z-dn.net/?f=u%20%3D%20g%28x%29%20%3D%20%5Cpi%20x)
![g^{\prime}(x) = \pi](https://tex.z-dn.net/?f=g%5E%7B%5Cprime%7D%28x%29%20%3D%20%5Cpi)
So
![y^{\prime} = f^{\prime}(u)*g^{\prime}(x)](https://tex.z-dn.net/?f=y%5E%7B%5Cprime%7D%20%3D%20f%5E%7B%5Cprime%7D%28u%29%2Ag%5E%7B%5Cprime%7D%28x%29)
![\frac{dy}{dx} = y^{\prime} = \sec^{2}(u)*\pi = \pi\sec^{2}{\pi x}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20y%5E%7B%5Cprime%7D%20%3D%20%5Csec%5E%7B2%7D%28u%29%2A%5Cpi%20%3D%20%5Cpi%5Csec%5E%7B2%7D%7B%5Cpi%20x%7D)