CONTINUOUS AND DISCONTINUOUS. HELP ME ANSWER THIS QUESTION

Question

1. At which values of x is the function f(x) = x^4-2x^3-3x^2 / x^4-5x^3+6x^2 continuous and discontinuous? State the answers from the least to the highest value, if there would be more than one. ANSWERS:

continuous at x = ________
discontinuous at x = ________ ; x=_________; x=__________

2. At which values of x is the function f(x) = x^2+x-6 / x-2 continuous and discontinuous?Answers:

continuous at x = ________
discontinuous at x = _________

Answer 1

f(x) = (x⁴-2x³-3x²) / (x⁴-5x³+6x²)

 

f is continuous for all x except where the denominator is zero.

 

x⁴ - 5x³ + 6x² = x²(x² - 5x + 6) = 0

 

                      = x²(x-3)(x-2) = 0

 

x = 0, 3, 2

 

f is discontinuous at x = 0, 2, 3

 

f is continuous for all other values of x.