Final answer:
To find the points of intersection between the functions f(x) = x + 1 and g(x) = (x + 1)(x - 5), set f(x) equal to g(x) and solve the resultant quadratic equation. The points of intersection are (6, 7) and (-1, 0).
Step-by-step explanation:
To find the points of intersection of the given functions, we need to set the two equations equal to each other and solve for x. For the first function, f(x) = x + 1, and for the second function, g(x) = (x + 1)(x - 5), let's solve for x when f(x) = g(x).
Step 1: Set f(x) = g(x).
x + 1 = (x + 1)(x - 5)
Step 2: Expand the right side.
x + 1 = x² - 5x + x - 5
Step 3: Simplify the equation.
x + 1 = x² - 4x - 5
Step 4: Move everything to one side to get a quadratic equation.
0 = x² - 5x - 6
Step 5: Factor the quadratic equation.
0 = (x - 6)(x + 1)
Step 6: Solve for x.
x = 6 and x = -1
Step 7: Find corresponding y-values by plugging x back into one of the original equations (we can use f(x) because it's simpler).
For x = 6: f(6) = 6 + 1 = 7
For x = -1: f(-1) = -1 + 1 = 0
Therefore, the points of intersection are (6, 7) and (-1, 0).