Given the functions f(x) = x^2 - 2x - 4 and g(x) = 2x - 4, at what values of x do f(x) and g(x) intersect?

* The values of x are 0 and 4

Step-by-step explanation:

* Lets explain how to solve the problem

- f(x) = x² - 2x - 4 is a quadratic function

- g(x) = 2x - 4

∵ f(x) and g(x) are intersected

∴ They meet each other in a point

- To find this point equate the two functions

∵ f(x) = g(x)

∵ f(x) = x² - 2x - 4

∵ g(x) = 2x - 4

∴ x² - 2x - 4 = 2x - 4 ⇒ subtract 2x from both sides

∴ x² - 4x - 4 = -4

- Add 4 to both sides

∴ x² - 4x = 0

- Take x as a common factor

∴ x(x - 4) = 0

- Equate each factor by 0

∴ x = 0

- OR

∴ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∴ f(x) and g(x) intersected at x = 0 and x = 4

* The values of x are 0 and 4