Thread: 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?

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 .

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:



Multiply both sides by to get rid of the fraction and move all terms to the LHS:



This is a quadratic equation in x². Use the substitution . The equation becomes:



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.