Answer: B (0.17, 2.33)
Step-by-step explanation:
A P E X
Answer:
g(x)
Step-by-step explanation:
y-intersect for h(x) is -11 as shown in the table, where the x value is 0
y-intersect for f(x) you find out by subbing 0 in the place of x and get the y intersect value of 2.99
y-intersect of g(x) is 3 as shown in the drawing
as seen across the three y-intersects, the value of g(x) y-intesect is the greatest
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
Answer:
8000 liters
Step-by-step explanation:
There are 1000 liters in a kiloliter, so you would multiply both sides by 8.
