<h2>
Hello!</h2>
The answers are:
![f(x)=\frac{5x+3}{2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B5x%2B3%7D%7B2%7D)
![f(x)=2x-8](https://tex.z-dn.net/?f=f%28x%29%3D2x-8)
![f(x)=7x-2](https://tex.z-dn.net/?f=f%28x%29%3D7x-2)
![f(x)=\frac{1}{x+2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7Bx%2B2%7D)
<h2>
Why?</h2>
To find the inverse function of a function, we need to replace the variable (x for this case) for the function itself (f(x)), where we see "x" we must rewrite with "y" or "f(x) and then, isolate "y" or "f(x). If we have the inverse function and we want to find the function, we need to reverse the process.
Let's find each function of the given inverse functions in order to match each one with its inverse.
First inverse function,
![f^{-1}(x)=\frac{2x-3}{5}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Cfrac%7B2x-3%7D%7B5%7D)
Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:
![x=\frac{2f(x)-3}{5}\\\\5x=2f(x)-3\\\\5x+3=2f(x)\\\\f(x)=\frac{5x+3}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2f%28x%29-3%7D%7B5%7D%5C%5C%5C%5C5x%3D2f%28x%29-3%5C%5C%5C%5C5x%2B3%3D2f%28x%29%5C%5C%5C%5Cf%28x%29%3D%5Cfrac%7B5x%2B3%7D%7B2%7D)
Therefore, the function that matches with the first inverse function is:
![f(x)=\frac{5x+3}{2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B5x%2B3%7D%7B2%7D)
Second inverse function,
![f^{-1}(x)=\frac{x+8}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Cfrac%7Bx%2B8%7D%7B2%7D)
Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:
![x=\frac{f(x)+8}{2}\\\\2x=f(x)+8\\\\2x-8=f(x)\\\\f(x)=2x-8](https://tex.z-dn.net/?f=x%3D%5Cfrac%7Bf%28x%29%2B8%7D%7B2%7D%5C%5C%5C%5C2x%3Df%28x%29%2B8%5C%5C%5C%5C2x-8%3Df%28x%29%5C%5C%5C%5Cf%28x%29%3D2x-8)
Hence, the function that matches with the second inverse function is:
![f(x)=2x-8](https://tex.z-dn.net/?f=f%28x%29%3D2x-8)
Third inverse function,
![f^{-1}(x)=\frac{x+2}{7}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Cfrac%7Bx%2B2%7D%7B7%7D)
Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:
![x=\frac{f(x)+2}{7}\\\\7x=f(x)+2\\\\7x-2=f(x)\\\\f(x)=7x-2](https://tex.z-dn.net/?f=x%3D%5Cfrac%7Bf%28x%29%2B2%7D%7B7%7D%5C%5C%5C%5C7x%3Df%28x%29%2B2%5C%5C%5C%5C7x-2%3Df%28x%29%5C%5C%5C%5Cf%28x%29%3D7x-2)
So, the function that matches with the third inverse function is:
![f(x)=7x-2](https://tex.z-dn.net/?f=f%28x%29%3D7x-2)
Fourth inverse function,
![f^{-1}(x)=\frac{1-2x}{x}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Cfrac%7B1-2x%7D%7Bx%7D)
Replacing "x" with "f(x)" and "f-1(x)" with "x" we have:
![x=\frac{1-2f(x)}{f(x)}\\\\xf(x)=1-2f(x)\\\\f(x)x+2f(x)=1\\\\f(x)(x+2)=1\\\\f(x)=\frac{1}{x+2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1-2f%28x%29%7D%7Bf%28x%29%7D%5C%5C%5C%5Cxf%28x%29%3D1-2f%28x%29%5C%5C%5C%5Cf%28x%29x%2B2f%28x%29%3D1%5C%5C%5C%5Cf%28x%29%28x%2B2%29%3D1%5C%5C%5C%5Cf%28x%29%3D%5Cfrac%7B1%7D%7Bx%2B2%7D)
So, the function that matches with the fourth inverse function is:
![f(x)=\frac{1}{x+2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7Bx%2B2%7D)
Have a nice day!
The percentages associated with each method on the pie-chart is as follows:
<h3>What is a pie chart?</h3>
- A <em>pie-chart</em> is a circular graph in which each region corresponds to a data, and the percentages of each data on the graph are associated to the percentages of the data.
In this problem, the regions are: Walk, Cycle, Car, Bus
- 30 out of 60 students walk, hence the percentage associated with Walk is:
![\frac{30}{60} \times 100\% = 50\%](https://tex.z-dn.net/?f=%5Cfrac%7B30%7D%7B60%7D%20%5Ctimes%20100%5C%25%20%3D%2050%5C%25)
- 5 out of 60 students cycle, hence the percentage associated with Cycle is:
![\frac{5}{60} \times 100\% = 8.3\%](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B60%7D%20%5Ctimes%20100%5C%25%20%3D%208.3%5C%25)
- 15 out of 60 students go by car, hence the percentage associated with Car is:
![\frac{15}{60} \times 100\% = 25\%](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B60%7D%20%5Ctimes%20100%5C%25%20%3D%2025%5C%25)
- 10 out of 60 students go by bus, hence the percentage associated with Bus is:
![\frac{10}{60} \times 100\% = 16.7\%](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B60%7D%20%5Ctimes%20100%5C%25%20%3D%2016.7%5C%25)
You can learn more about a pie-chart at brainly.com/question/25793130
Answer:
Its 225
Step-by-step explanation:
1200 divided by 225 is 3
Answer:
Esther is right. Take the cash today
Step-by-step explanation:
The value of money tends to decrease due to inflation. With GH¢1000 now, she can invest and work to earn more herself.
Answer: No triangle can be drawn.
Step-by-step explanation:
According to the triangle Inequality theorem, the sum of any two sides of a triangle must be greater than the third side.
If the measurements of triangle taken as 2 cm, 3 cm, and 5 cm , no triangle can be formed because 2+3=5 which does not satisfy the triangle inequality.
If the measurements of triangle taken as 2 cm, 3 cm, and 8 cm , no triangle can be formed because 2+3=5<8 which does not satisfy the triangle inequality.
Hence, No triangle can be drawn.