# Thread: finding intersection of two functions

1. ## 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?

2. 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 $x^2 - 1 = \frac{x^2}{x^2 + 1}$.

3. 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:

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

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

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

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

$u^2-u-1=0$

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.