Question

Find the domain of the real valued function: f(x) = $\sqrt{x^{2} - 3x + 2}$

Answer 1

Answer:   Domain = R - ( 1 , 2 )

The given function is

$\sqrt{x^{2}-3x+2}$

It is not valid for

x² - 3 x + 2 < 0

x² - 2 x - x + 2 < 0

x(x - 2) -1 (x -2) < 0

(x - 2)(x -1) < 0

It is possible in TWO cases

(x - 2) < 0 and (x -1) > 0          OR           (x - 2) > 0 and (x -1) < 0

x < 2 and x > 1                       OR           x > 2 and x < 1  (It is not possible)  

⇒  1 < x < 2

Domain = R - ( 1 , 2 )

Answer 2

Answer:

domain of f(x) is x ≤ 1 or x ≥ 2

Step-by-step explanation:

To find the domain of the real valued function:

$f(x) =  \sqrt{x^{2} - 3x + 2}$

first factorise x²-3x+2

⇒ x²-2x-x+2

⇒ x(x-2)-1(x-2)

⇒ (x-1)(x-2)

as we know that √(x²-3x+2) ≥0

so (x-1)(x-2)≥0

x-1≥0

x ≤ 1

or x-2≥0

x ≥ 2

so domain of f(x) is x ≤ 1 or x ≥ 2