The cuic equation is -1 and 2i
43, 47, is the composite numbers between 41 and 50
Answer: They are inverses of each other
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Explanation:
We'll need to compute h(f(x)) and f(h(x)) to see if we get x each time.
![h(x) = 9x-4\\\\h(f(x)) = 9(f(x))-4\\\\h(f(x)) = 9\left(\frac{x+4}{9}\right)-4\\\\h(f(x)) = x+4-4\\\\h(f(x)) = x\\\\](https://tex.z-dn.net/?f=h%28x%29%20%3D%209x-4%5C%5C%5C%5Ch%28f%28x%29%29%20%3D%209%28f%28x%29%29-4%5C%5C%5C%5Ch%28f%28x%29%29%20%3D%209%5Cleft%28%5Cfrac%7Bx%2B4%7D%7B9%7D%5Cright%29-4%5C%5C%5C%5Ch%28f%28x%29%29%20%3D%20x%2B4-4%5C%5C%5C%5Ch%28f%28x%29%29%20%3D%20x%5C%5C%5C%5C)
and,
![f(x) = \frac{x+4}{9}\\\\f(h(x)) = \frac{h(x)+4}{9}\\\\f(h(x)) = \frac{9x-4+4}{9}\\\\f(h(x)) = \frac{9x}{9}\\\\f(h(x)) = x\\\\](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7Bx%2B4%7D%7B9%7D%5C%5C%5C%5Cf%28h%28x%29%29%20%3D%20%5Cfrac%7Bh%28x%29%2B4%7D%7B9%7D%5C%5C%5C%5Cf%28h%28x%29%29%20%3D%20%5Cfrac%7B9x-4%2B4%7D%7B9%7D%5C%5C%5C%5Cf%28h%28x%29%29%20%3D%20%5Cfrac%7B9x%7D%7B9%7D%5C%5C%5C%5Cf%28h%28x%29%29%20%3D%20x%5C%5C%5C%5C)
Both composite functions lead to x each time.
The equations h(f(x)) = x and f(h(x)) = x being true means each function is the inverse of the other.
Answer:
1. $361800
Step-by-step explanation:
Given,
principle balance=$670
interest rate=8%
![A=P(1+\frac{r}{n})(nt)](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%28nt%29)
A= Final amount
P= initial Principal balance
r= interest rate
n= number of times interest applied per time period
t= number of times period elapsed
compound interest formula,![A=670(1+\frac{8}{1})(60) )\\A=361800](https://tex.z-dn.net/?f=A%3D670%281%2B%5Cfrac%7B8%7D%7B1%7D%29%2860%29%20%29%5C%5CA%3D361800)
Therefore the Present value is $361800