Need a strategy for inverting a function

In summary, the conversation was about solving for y in an equation involving constants K(1) and K(2). One person suggested squaring both sides to turn it into a cubic equation and then solving for y=0, but later realized that this was not the correct solution. The correct solution involves using a formula for solving cubic equations, and only one of the three possible solutions avoids using imaginary numbers.
  • #1
MCarroll
9
0
I can't solve for y from:

x = - [tex]K_{1}[/tex]* y *[tex]\sqrt{K_{2}-y}[/tex]

where K(1) and K(2) are constants.

I am pretty sure as a younger man I was taught how to do this but I can't remember the strategies I can/should use. Any thougths would be very appreciated.
 
Last edited:
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  • #2
Square both sides and you get a cubic in y, out of which the solution y=0 is evident, so you've only got a simple quadratic to solve.
 
  • #5
Thanks, and genneth I'm not one to talk!

Shooting Star, It looks from the page you sent that the general form is:

y = 3f/[-e+(e3-27f2)1/3],
y = 3f/[-e+(e3-27f2)1/3(-1+sqrt[-3])/2],
y = 3f/[-e+(e3-27f2)1/3(-1-sqrt[-3])/2].

so only the first of these avoids i, right?
 

What is the purpose of inverting a function?

Inverting a function allows us to find the input value that corresponds to a given output value. This can be useful in many applications, such as finding the original number from a percentage or calculating the inverse of a mathematical operation.

What are the steps involved in inverting a function?

The first step is to express the function in terms of y instead of x. Then, switch the x and y variables, making y the subject of the equation. Finally, solve for y to get the inverse function.

What are the common challenges in inverting a function?

One challenge is that not all functions have an inverse. This can happen when the original function is not one-to-one, meaning that multiple inputs can result in the same output. Another challenge is that the inverse function may not be easily solvable, especially for more complex functions.

How can I check if my inverse function is correct?

To check if your inverse function is correct, you can use the composition test. This involves plugging the original function into the inverse function and vice versa. If the result is x for both tests, then the inverse function is correct.

How can I use an inverted function in real-world applications?

Inverted functions can be used in many real-world scenarios, such as finding the original value of a discounted price, calculating the dose of a medication based on its concentration, or determining the amount of time needed to reach a certain distance while driving at a given speed. They can also be used in engineering and scientific calculations.

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