Thread: Intersection of Functions

I need help finding the points at which the following 2 functions intersect:

f(x) = 1/x
g(x) = -x^2 + 4x - 2

for x>0

I figured out that x=1 was a solution, by inspection, but I cannot solve for the other one.

Originally Posted by kaiser0792

I need help finding the points at which the following 2 functions intersect:

f(x) = 1/x
g(x) = -x^2 + 4x - 2

for x>0

I figured out that x=1 was a solution, by inspection, but I cannot solve for the other one.

calculate the equation for


so,
=

I realize that I need to set f(x) equal to g(x), but I'm not able to solve the resulting equation for x.

Clearly we need to factor the right-hand side to find the solutions. You already know is a factor because you said that is a solution. So, use polynomial long division (or synthetic division) to factor and find the other solutions.

Thanks, I forgot about dividing out the known factor.