Question

find to domain of the function√x^2-3x+2​

Answer 1

Answer :

(-∞ , 1] U [2 , ∞)

Solution :

Let the given function be f(x) .

Thus ,

f(x) = √(x² - 3x + 2)

The given function f(x) will be a real valued function if ,

=> x² - 3x + 2 ≥ 0

=> x² - x - 2x + 2 ≥ 0

=> x(x - 1) - 2(x - 1) ≥ 0

=> (x - 1)(x - 2) ≥ 0

Here ,

Two cases arises :

1) x - 1 ≥ 0 and x - 2 ≥ 0

OR

2) x - 1 ≤ 0 and x - 2 ≤ 0

• Case1 : x - 1 ≥ 0 and x - 2 ≥ 0

=> x ≥ 1 and x ≥ 2

=> x ≥ 2

=> x € [2 , ∞)

OR

• Case2 : x - 1 ≤ 0 and x - 2 ≤ 0

=> x ≤ 1 and x ≤ 2

=> x ≤ 1

=> x € (-∞ , 1]

Thus ,

The domain of the given function will be given as ; x € (-∞ , 1] U [2 , ∞)