Could you take another photo with you zoomed a lil bit more so I can answer it?
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
.
So, we can write the given integral as

Splitting up terms and replacing
in the first integral, we get

Answer: The correct option is (A). 3.
Step-by-step explanation: We are given to find the scale factor of dilation from ΔABC to ΔDEF.
As shown in the figure, the lengths of the sides of ΔABC to ΔDEF are
AB = 5 units, BC = 4 units, CA = 3 units,
DE = 15 units, EF = 12 units, FD = 9 units.
We know that the scale factor is given by

Therefore, the scale factor of dilation from from ΔABC to ΔDEF is

Thus, the required scale factor is 3.
Option (A) is correct.
Answer:
c. Korey will see an overall profit in his third year of business
Step-by-step explanation:
His cost for first year
= 12500+8000
=$ 20500
Profit first year= $12000
Net Profit first year= -$8500
Second year cost= $8000
Profit second year
= 12000+12000(0.06)
= 12000+720
=$ 12720
Net profit second year = -8500+12720-8000
= -3780
Third year
Cost = $8000
Profit= 12720+12720(0.06)
Profit=$13483.2
Net profit= 13483.2-8000-3780
Net profit= $1703.2