Real Slice of Mandelbrot set

I'm trying to prove that the real slice of a Mandelbrot set is M n R =[-2,1/4]

I've tried researching it on the internet but everything I find seems to just state this and not prove it.

The hint I've been given to start is is to let

(1/4, ) proving that for each that 1/4

where

Any help would be greatly appreciated

Re: Real Slice of Mandelbrot set

What you have written makes no sense. For any real number c, f_{c}(z)- z is a complex number. You cannot say it is "larger than c- 1/4, a real number.

Perhaps you meant ?