Final answer:
To solve f(x) = g(x), rearrange the equations and use the quadratic formula to solve for x. The solutions are x = 5 and x = -7, giving the points of intersection of f(x) and g(x).
Step-by-step explanation:
To solve the equation f(x) = g(x), we need to find the values of x that make the two functions equal. Setting the two functions equal, we have:
x^2 - x + 3 = 2x^2 - 3x - 32
Combining like terms and rearranging, we get:
x^2 + 2x - 35 = 0
Now we can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Plugging in the values a = 1, b = 2, and c = -35, we get:
x = (-2 ± sqrt(2^2 - 4(1)(-35))) / (2(1))
x = (-2 ± sqrt(4 + 140)) / 2
x = (-2 ± sqrt(144)) / 2
x = (-2 ± 12) / 2
So the two solutions for x are x = 5 and x = -7. Therefore, the points of intersection of f(x) and g(x) are (5, f(5)) and (-7, f(-7)).