Final answer:
To find the points of intersection between f(x) and g(x), set them equal and solve for x, which yields x-values where they intersect. By solving 5x² + 9 = 8x + 12, we get the x-values -1/5 and 3, which can be used to find the corresponding y-values.
Step-by-step explanation:
To solve for x when f(x) = g(x), we must set the two functions equal to each other and solve the resulting equation. This will give us the x-values at which the graphs of the two functions intersect.
The given functions are f(x) = 5x² + 9 and g(x) = 8x + 12. Setting these equal to each other:
5x² + 9 = 8x + 12
To solve for x, we first bring all terms to one side of the equation:
5x² - 8x + 9 - 12 = 0
5x² - 8x - 3 = 0
Now we factor the quadratic equation or use the quadratic formula to solve for x:
(5x + 1)(x - 3) = 0
Setting each factor equal to zero gives two solutions for x:
5x + 1 = 0 which gives x = -1/5
x - 3 = 0 which gives x = 3
Thus, we have two points of intersection, and we can plug these x-values into either of the original functions to find the corresponding y-values and complete the intersection points.