9514 1404 393
Answer:
1) f⁻¹(x) = 6 ± 2√(x -1)
3) y = (x +4)² -2
5) y = (x -4)³ -4
Step-by-step explanation:
In general, swap x and y, then solve for y. Quadratics, as in the first problem, do not have an inverse function: the inverse relation is double-valued, unless the domain is restricted. Here, we're just going to consider these to be "solve for ..." problems, without too much concern for domain or range.
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1) x = f(y)
x = (1/4)(y -6)² +1
4(x -1) = (y-6)² . . . . . . subtract 1, multiply by 4
±2√(x -1) = y -6 . . . . square root
y = 6 ± 2√(x -1) . . . . inverse relation
f⁻¹(x) = 6 ± 2√(x -1) . . . . in functional form
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3) x = √(y +2) -4
x +4 = √(y +2) . . . . add 4
(x +4)² = y +2 . . . . square both sides
y = (x +4)² -2 . . . . . subtract 2
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5) x = ∛(y +4) +4
x -4 = ∛(y +4) . . . . . subtract 4
(x -4)³ = y +4 . . . . . cube both sides
y = (x -4)³ -4 . . . . . . subtract 4
To solve this problem you must apply the proccedure shown below:
1. Clear the radius from the formula for the circumference of a circle and substitute values, as following:
2. Substitute the radius calculated into the formula for calculate the surface area of the sphere:
The answer is: 
Amount of Interest = $36
Rate of interest = 3% per annum
Total time period for which the money was invested = 3 years
Let us assume the Principal amount = x
Then
Interest = Principal * Rate of Interest * time
36 = x * 3% * 3
36 = 9x/100
36 * 100 = 9x
3600 = 9x
x = 3600/9
= 400
So the initial sum of the money that was invested was $400.
Https://photomath.net/s/P56lb
The link will show you how to solve the problem but if you still don't get it you download the app Photomath and it will give you more detailed steps.
