# Fixed points

1. May 12, 2009

### morbello

ive got a question on how to get a fixed point. on the equation for.

$$\frac{1}{8}X^2+\frac{11}{8}X+\frac{1}{2}$$

do you find the two factors to get the fixed points. or run the equation though a quadratic formula to get the fixed points.

i have an = which is x^2-3X-4=0 but i dont know how the fraction 11/8X =3X in the equation.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
A fixed point for a function, f, is a value of x such that f(x)= x.
Here
$$f(x)= \frac{1}{8}X^2+\frac{11}{8}X+\frac{1}{2}= x$$
The easiest way to handle the fractions is to multiply the entire equation by 8:
$$x^2+ 11x+ 1= 8x$$
or
$$x^2+ 3x+ 1= 0$$

Last edited by a moderator: May 12, 2009
2. May 12, 2009

### Tom Mattson

Staff Emeritus
Yes, that's how you do it. But I wouldn't use both $X$ and $x$ for the variable. Use the same symbol in each instance.

3. May 13, 2009