Hello,
I have a function to inverse, I proved that thise function is inversible but I didn't manage to find the expression of the inverse:
here is the function:
y= ((P1*A*r^(-alpha))/(N+(P2*A*(r^2-2*R*cos(theta)*r+R^2)^(-alpha/2))))
the function is decreasing for r< R/cos(theta)
so I have to find the expression of 'r' in function of y,P1, P2, alpha, N, R.
all the parameters here are positive; and r<R/cos(theta).
I used matlab (with 'solve' function) but it didn't manage to inverse this function.
Thanks for your precious help
And what is the independent variable? In other words, to find the inverse function, what should we solve for? r? ?
If the problem is to solve for , this is relatively straight forward. Multiply both sides by the denominator: .
Take the power of both sides:
Multiply both sides by :
Subtract N from both sides:
Divide both sides by :
Subtract from both sides:
Finally, divide both sides by -2R:
and take the arccosine of both sides:
:
If you want to solve for r, having both and makes it much harder.