Here are the functions:

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

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

how do i find the intersecrions?

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- Mar 15th 2010, 02:02 AMAnemorifinding 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 AMmr fantastic
- Mar 15th 2010, 02:18 AMearboth
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.