# Newton-Raphson method for y=1/f(x)

1. Jul 15, 2004

### Peter_F

I need to know the Newton-Raphson equation for y=1/f(x)

I've tried to work it out, but I'm not sure if I'm right

I got this:

x = x + f'(x) / f(x)

EDIT> I've tried what I worked out and realised that it's horribly wrong.
I really need help :P

Another edit>
I don't understand why it's not working :'( I see what was wrong with what I originally got. I just made a simple mistake, but now I've got something which I'm sure is right, but won't work.

y = f(x) = 1 / g(x)

Newton Raphson:

x = x - f(x) / f'(x)
= x - (1/g(x)) / (-g'(x)/g(x)^2)
= x - g(x)^2 / -g'(x) * g(x)
= x - g(x) / -g'(x)
= x + g(x) / g'(x)

I tried this too, and it didn't work.
I'm using this in a computer program, so I need to know if I'm using the wrong equation, or if a different part of the program is messing it up.

Yet another edit> I don't need this any more. I did something different instead. Sorry for the waste of time :P

Last edited: Jul 16, 2004
2. Jul 16, 2004

### krab

I don't really understand the formulation of the problem. Newton-Raphson is for finding the solution x of the equation f(x)=0. What do you mean by y=1/f(x)? What is there to solve for?

3. Jul 16, 2004

### Zurtex

As krab says, the method is for approximating a solutions to f(x) = 0.

1 / f(x) will never equal 0.