Question

Based on the graph below, what is the solution to the equation f(x) = g(x)?

Answer 1

The wording of the second function may be interpreted in several differente ways. These are some:

g(x) = (x^2 +2)(x-8)
g(x)=x^2 + 2(x-8)
g(x) x^2 +2x - 8

I will work with the last one, so my system of equation is:

f(x) = - x +2.5
g(x) = x^2 + 2x - 8

f(x) = g(x) ⇒ - x + 2.5 = x^2 + 2x - 8

x^2 + 3x - 8 - x - 2.5 = 0

x^2 + 3x - 10.5 = 0

Use the quadratic formula to solve for x:

x = [ - 3 +/- √(3^2) - 4(1)(-10.5) ]/2

x = - 5.07 and x = 2.07