Question

find the domain of the following functions (i) f(x) =x/x^2+3x+2

Answer 1

EXPLANATION.

Domain of the functions.

⇒ f(x) = x/(x² + 3x + 2).

As we know that,

Factorizes the denominator of the equation, we get.

⇒ x² + 3x + 2.

Factorizes the equation into middle term splits, we get.

⇒ x² + 2x + x + 2.

⇒ x(x + 2) + 1(x + 2).

⇒ (x + 1)(x + 2).

Now, we can write equation as,

⇒ f(x) = x/(x + 1)(x + 2).

Denominator : x² + 3x + 2 ≠ - 1, - 2.

Domain = x ∈ R - {-1, -2}.

Answer 2

$\huge\mathcal{\fcolorbox{aqua}{azure} {\red{ Question}}}$

find the domain of the following functions (i) f(x) =x/x^2+3x+2

$\huge\mathcal{\fcolorbox{aqua}{azure} {\red{ Answer}}}$

$\color{voilet}\huge{Factorise}$

x² + 3x + 2

Factorise The equation into middle terms.

= x² + 2x + x + 2

= x (x + 2) + 1( x + 2)

= (x + 1) (x + 2)

$\color{voilet}\huge{Equation}$

= f(x) = x/(x+1) (x+2)

$\color{voilet}\huge{Dominator}$

x² + 3x + 2 = -1 , -2.

Domain is

$\color{voilet}\huge{-1,-2}$