find the inverse:
Y=(x-3.21)(14700 - 3040x)
to find the inverse, interchange the x and y variables, so
x = (y-3.21)(14700 - 3040y)
You have a quadratic function, which is not a one-to-one function, unless the domain is restricted, and it is not here.
http://www.wikihow.com/Find-the-Inverse-of-a-Quadratic-Function
Inverses of funcions which are not one-to-one do not exist.
To find the inverse of a function, we need to switch the positions of the variables x and y and solve for y.
The original equation is:
Y = (x - 3.21)(14700 - 3040x)
Step 1: Swap x and y.
x = (y - 3.21)(14700 - 3040y)
Step 2: Solve for y.
Expand the equation and rearrange it to the standard quadratic form:
14700x - 3040x^2 = y - 3.21 - 14700y + 3040y^2
3040y^2 - 14700y + 3.21 + 3040x^2 - 14700x = 0
Step 3: Rearrange the equation and combine like terms.
3040x^2 - 14700x + 3040y^2 - 14700y + 3.21 = 0
Step 4: Solve for y using the quadratic formula.
The quadratic formula is given by:
y = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 3040, b = -14700, and c = 3040x^2 + 3.21.
Substituting these values into the quadratic formula, we get:
y = (14700 ± √((-14700)^2 - 4(3040)(3040x^2 + 3.21))) / (2 * 3040)
Simplifying further:
y = (14700 ± √(216090000 - 36966400x^2 - 38464.32)) / 6080
y = (14700 ± √(215651535 - 36966400x^2)) / 6080
Therefore, the inverse of the function Y = (x - 3.21)(14700 - 3040x) is:
y = (14700 ± √(215651535 - 36966400x^2)) / 6080