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.