Question 809715: The formula for the area of a circle is A=3.14r2. Find the inverse of the function. Use the inverse to find the radius of the circle whose area is 36 square centimeters.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
You assert that the formula for the area of a circle is  . The assertion is not entirely true.  is the formula for the area of a circle, whereas is a formula for an approximation of the area of a circle.
Also, if you just want to be able to determine the radius given the area, you want to solve the equation for  in terms of  and  . But that is only half the process of finding a function inverse, so your instruction to "Find the inverse of the function" certainly can be done, but you would not be able to use the inverse function to calculate the radius given the area.
Allow me to illustrate:
Your function with as the independent variable:
\ =\ 3.14r^2)
The process of finding the inverse is as follows:
Change the function designator to a simple variable representing the value of the function on a Cartesian plane. We might just as well use in this case:
Multiply both sides by  :
Take the square root of both sides:
Note that we can ignore the negative root because we are dealing with a length measurement and a negative value would be meaningless. Just for neatness sake, swap sides:
Now, the above is the equation you need in order to calculate an approximation of the radius given the area. But the above equation is most certainly NOT the inverse of the original function. The inverse function is found by taking the above, swapping the variables and then replacing the function value variable with the original function designator with a -1 superscript:
\ =\ \sqrt{\frac{r}{3.14}})
This inverse really has no meaning in a physical sense, but it does follow the definition of an inverse of a function and it cannot, under any circucmstances, be used to perform the calculation asked for in the last part of your question. I don't know where you got the language you used in your question, but whoever taught that to you was playing mighty fast and loose with established definitions.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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