Find the inverse of “f” algebraically, please!

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Here are the steps to find the inverse

Now this would be the answer if our original domain was

However, that's not the case and instead our domain is

Reflecting any (x,y) point in this domain restriction, over the the line y = x, will have us land on a point with a negative y value. This is because the inverse will swap the x and y values.

Therefore, the inverse function must ultimately be negative.

Currently is positive since the result of any square root is never negative.

To fix this, we stick a negative out front to get the final answer being

207/8 is the right

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.