Answer: 1/x + 7
Step-by-step explanation: you plug the function g(x) into the function f(x) .. substitue g(x) for the x in f(x)
G(x) = 1/x , so you plug that in the x of f(x) and get 1/x + 7
Answer:
Step-by-step explanation:
Let :
C = number of cats
D = number of dogs
Raul's pet store has a play area that can fit up to 30 cats and dogs.
C + D = 30
The pet store never has more than 8 cats in the play areas.
<h2>
C < 9</h2>
(there can never be 9 or more cats)
As or the number of dogs :
C + D = 30
C = 30 - D
Since we know that C < 9. To get the number of dogs allowed, we just plug in 30 - D for C.
30 - D < 9
30 - 9 < D
or
<h2>
D > 21</h2>
(dogs have to be 22 or more)
Answer: 3:35
Step-by-step explanation:
Answer:
1982.71 mL
Step-by-step explanation:
1 qt = 946.353 mL
2 qt = 1982.71 mL
If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show
Let 
. Compute the inverse:
![f\left(f^{-1}(x)\right) = \sqrt{1 + f^{-1}(x)^3} = x \implies f^{-1}(x) = \sqrt[3]{x^2-1}](https://tex.z-dn.net/?f=f%5Cleft%28f%5E%7B-1%7D%28x%29%5Cright%29%20%3D%20%5Csqrt%7B1%20%2B%20f%5E%7B-1%7D%28x%29%5E3%7D%20%3D%20x%20%5Cimplies%20f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%5E2-1%7D)
and we immediately notice that ![f^{-1}(x+1)=\sqrt[3]{x^2+2x}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%2B1%29%3D%5Csqrt%5B3%5D%7Bx%5E2%2B2x%7D)
.
So, we can write the given integral as
Splitting up terms and replacing 
in the first integral, we get
