Can you show the mentioned diagram?
        
             
        
        
        
Answer:
The functions are inverses; f(g(x)) = x ⇒ answer D
 ⇒ answer D
 ⇒ answer D
Step-by-step explanation:
* <em>Lets explain how to find the inverse of a function</em>
- Let f(x) = y
- Exchange x and y
- Solve to find the new y
- The new y = 
* <em>Lets use these steps to solve the problems</em>
∵ 
∵ f(x) = y
∴ 
- Exchange x and y
∴ 
- Square the two sides
∴ x² = y - 3
- Add 3 to both sides
∴ x² + 3 = y
- Change y by 
∴ 
∵ g(x) = x² + 3
∴ 
∴ <u><em>The functions are inverses to each other</em></u>
* <em>Now lets find f(g(x))</em>
- To find f(g(x)) substitute x in f(x) by g(x)
∵ 
∵ g(x) = x² + 3
∴ 
∴ <u><em>f(g(x)) = x</em></u>
∴ The functions are inverses; f(g(x)) = x
* <em>Lets find the inverse of h(x)</em>
∵ h(x) = 3x² - 1 where x ≥ 0
- Let h(x) = y
∴ y = 3x² - 1
- Exchange x and y
∴ x = 3y² - 1
- Add 1 to both sides
∴ x + 1 = 3y²
- Divide both sides by 3
∴ 
- Take √ for both sides
∴ ± 
∵ x ≥ 0 
∴ We will chose the positive value of the square root
∴ 
- replace y by 
∴ 
 
        
             
        
        
        
If the scholarship pays 75% of her classes cost, that means that she has to pay the 25% remaining of the classes cost so if we calculate it as follow:
0.25 * $14,000 = $3,500 
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Another method to understand:
if the scolarship pays 75% of her classes that will be 
0.75* $14,000 = $10,500
now she has to pay the remaining of the total cost and that will be 
$14,000 - $10,500 = $3,500.
        
             
        
        
        
The total number of possible fivey sequences are; 6
<h3>How to solve a sequence?</h3>
We are told we are dealing with a fivey sequence which means that all the terms of the sequence must be positive integers and they must add up to 5.
Now, the possible numbers that can be used are;
1, 2 and 3.
If we start with 3, number of possible sequences is; 1
If we start with1, number of possible sequences is; 3 ways
If we start with 2, number of possible sequences is; 2 ways
Thus;
Total number of fivey sequences is 1 + 2 + 3 = 6 possible sequences
Read more about Sequence at; brainly.com/question/13612968
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