finding intersection of two functions

• Mar 15th 2010, 02:02 AM
Anemori
finding intersection of two functions
Here are the functions:

(G of k)(x) = x^2-1

f(x) = x^2/(x^2+1)

how do i find the intersecrions?
• Mar 15th 2010, 02:11 AM
mr fantastic
Quote:

Originally Posted by Anemori
Here are the functions:

(G of k)(x) = x^2-1

f(x) = x^2/(x^2+1)

how do i find the intersecrions?

Start by solving $\displaystyle x^2 - 1 = \frac{x^2}{x^2 + 1}$.
• Mar 15th 2010, 02:18 AM
earboth
Quote:

Originally Posted by Anemori
Here are the functions:

(G of k)(x) = x^2-1

f(x) = x^2/(x^2+1)

how do i find the intersecrions?

The values of the functions must be equal at the point of intersection. Thus:

$\displaystyle x^2-1=\dfrac{x^2}{x^2+1}$

Multiply both sides by $\displaystyle x^2+1$ to get rid of the fraction and move all terms to the LHS:

$\displaystyle x^4-x^2-1=0$

This is a quadratic equation in x². Use the substitution $\displaystyle u = x^2~\implies~|x|=\sqrt{u}$. The equation becomes:

$\displaystyle u^2-u-1=0$

Solve for u, afterwards determine x, plug in the value of x in one of the equations of a function to calculate the y-coordinate of the point of intersection.