Step-by-step explanation:
f(x) = (3/2)ˣ
g(x) = (2/3)ˣ
These are examples of exponential equations:
y = a bˣ
If b > 1, the equation is exponential growth.
If 0 < b < 1, the equation is exponential decay.
So f(x) is an example of exponential growth, and g(x) is an example of exponential decay.
Also, 2/3 is the inverse of 3/2, so:
g(x) = (3/2)^(-x)
So more specifically, f(x) and g(x) are reflections of each other across the y-axis.
Answer:
If that dot in the middle is the middle of the circle, then that should mean the center is 5 away from both of those lines. Therefore, I believe x would 9/2 or 4.5
General Idea:
Domain of a function means the values of x which will give a DEFINED output for the function.
Applying the concept:
Given that the x represent the time in seconds, f(x) represent the height of food packet.
Time cannot be a negative value, so
The height of the food packet cannot be a negative value, so
We need to replace 
for f(x) in the above inequality to find the domain.
![-15x^2+6000\geq 0 \; \; [Divide \; by\; -15\; on\; both\; sides]\\ \\ \frac{-15x^2}{-15} +\frac{6000}{-15} \leq \frac{0}{-15} \\ \\ x^2-400\leq 0\;[Factoring\;on\;left\;side]\\ \\ (x+200)(x-200)\leq 0](https://tex.z-dn.net/?f=%20-15x%5E2%2B6000%5Cgeq%200%20%5C%3B%20%5C%3B%20%20%5BDivide%20%5C%3B%20by%5C%3B%20-15%5C%3B%20on%5C%3B%20both%5C%3B%20sides%5D%5C%5C%20%5C%5C%20%5Cfrac%7B-15x%5E2%7D%7B-15%7D%20%2B%5Cfrac%7B6000%7D%7B-15%7D%20%5Cleq%20%5Cfrac%7B0%7D%7B-15%7D%20%5C%5C%20%5C%5C%20x%5E2-400%5Cleq%200%5C%3B%5BFactoring%5C%3Bon%5C%3Bleft%5C%3Bside%5D%5C%5C%20%5C%5C%20%28x%2B200%29%28x-200%29%5Cleq%200%20)
The possible solutions of the above inequality are given by the intervals ![(-\infty , -2], [-2,2], [2,\infty )](https://tex.z-dn.net/?f=%20%28-%5Cinfty%20%2C%20-2%5D%2C%20%5B-2%2C2%5D%2C%20%5B2%2C%5Cinfty%20%29%20)
. We need to pick test point from each possible solution interval and check whether that test point make the inequality 
true. Only the test point from the solution interval [-200, 200] make the inequality true.
The values of x which will make the above inequality TRUE is 
But we already know x should be positive, because time cannot be negative.
Conclusion:
Domain of the given function is 
Answer: -2a + 3b
Solution:
3b - 2a
Simplify
= -2a + 3b
2/3 + 1/4. You start by converting the fractions so that they have a common denominator.
8/12 + 3/12 = 11/12
11/12 of the girls have blue and brown eyes. That leaves 1/12 of the girls who have neither blue nor brown eyes.
