Question

Solve: f(x) = {(x – 1)×(2 – x)}/(x – 3) ≥ 0

Answer 1

Answer:

x∈[1,2]∪[3,∞)

Step-by-step explanation:

is a cubic with positive leading coefficient and zeros of multiplicity 1 at x=1,and

and x=3.

As a result:

f(x) is continuous.

f(x) is positive for large positive values of x.

f(x) is negative for large negative values of x.

f(x) changes sign at each of its zeros.

Hence

f(x) is non-negative in the intervals 1,2] and [3,∞)

graph{x^3-6x^2+11x-6 [-3.397, 6.603, -2.24, 2.76]}