<h2>
Answer:</h2><h3>False</h3><h2>
Step-by-step explanation:</h2>
Let's find the inverse function of 
to know whether this function has an inverse function ![f^{-1}(x)=-3+\sqrt[3]{x+4}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D-3%2B%5Csqrt%5B3%5D%7Bx%2B4%7D)
. So let's apply this steps:
a) Use the Horizontal Line Test to decide whether 
has an inverse function.
Given that f(x) is a cubic function there is no any horizontal line that intersects the graph of at more than one point. Thus, the function is one-to-one and has an inverse function.
b) Replace 
by 
in the equation for .
c) Interchange the roles of 
and and solve for
![x=(y-3)^3+4 \\ \\ \therefore x-4=(y-3)^3 \\ \\ \therefore (y-3)^3=x-4 \\ \\ \therefore y-3=\sqrt[3]{x-4} \\ \\ \therefore y=\sqrt[3]{x-4}+3](https://tex.z-dn.net/?f=x%3D%28y-3%29%5E3%2B4%20%5C%5C%20%5C%5C%20%5Ctherefore%20x-4%3D%28y-3%29%5E3%20%5C%5C%20%5C%5C%20%5Ctherefore%20%28y-3%29%5E3%3Dx-4%20%5C%5C%20%5C%5C%20%5Ctherefore%20y-3%3D%5Csqrt%5B3%5D%7Bx-4%7D%20%5C%5C%20%5C%5C%20%5Ctherefore%20y%3D%5Csqrt%5B3%5D%7Bx-4%7D%2B3)
d) Replace by 
in the new equation.
![f^{-1}(x)=\sqrt[3]{x-4}+3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Csqrt%5B3%5D%7Bx-4%7D%2B3)
So this is in fact the inverse function and it isn't the same given function. Therefore, the statement is false
Given that the certain type of spore colony having 50 spores
and a rate of growth of 3 times in 24 hour or one day period, it would grow to
(3 times 50) 150 spores at the end of the first day, (3 times 150) 450 in the 2nd
day, (3 times 450) 1350 in the third day, and (3 times 1350) 4050 spores at
the end of the fourth day.
Answer:
10 km/hr
Step-by-step explanation:
The aircraft carrier and the container ship both took 30 hours to travel their respective distances. If you divide both numbers by 30, you find that their differences is 5. We can tell that the aircraft carrier traveled 450 ÷ 30 = 15 km/hr and the container ship traveled at a speed of 300 ÷ 30 = 10 km/hr. The aircraft carrier traveled 5 km/hr faster. So, we can tell the container ship traveled at 10 km/hr.
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Part A
1 hour would be $14.95+$12.95 (entrance fee)= $27.90
2 hours 14.95(2)+12.95=$42.85
3 hours 14.95(3)+12.95=$57.80
4 hours 14.95(4)+12.95=$72.75
Part B
No, because the totally price also includes the price of the entrance fee. In order to find the number of hours spent horseback riding you will first need to subtract the entrance fee then divide by the price per hour.
