Question

find the domain of the following f(x)=x²+2x+1 / x²-8x+12​

Answer 1

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

$\star \: \: {\sf{ f(x) = \frac{ {x}^{2} + 2x + 1 }{ {x}^{2} + 8x + 12} }}$

${\bf{\blue{\underline{To\:Find:}}}}$

• Domain=?

${\bf{\blue{\underline{Now:}}}}$

For f to be defined,

$: \implies{\sf{ {x}^{2} - 8x + 12 \neq0 }}$

$: \implies{\sf{ {x}^{2} - 6x - 2x+ 12 \neq0 }}$

$: \implies{\sf{ {x} (x- 6) - 2(x - 6) \neq0 }}$

$: \implies{\sf{ (x- 2) (x - 6) \neq0 }}$

$: \implies{\sf{ x \neq2,6 }}$

Now f is defined for real numbers except 2,6

$\dagger \:\boxed{\sf{ D_{ f} = <strong>R</strong> - \{{ 2,6 \}} \: }}$

Answer 2

SOLUTION ⚜️

$given \: f(x) = \frac{ {x}^{2} + 2x + 1 }{ {x}^{2} - 8x + 12}$

Here, f(x) is an rational function of x as$\frac{ {x}^{2} + 2x + 1 }{ {x}^{2} - 8x + 12}$is rational expression.

$\therefore f(x) \: assumes \: real \: values \: x \: espects \\ for \: the \: values \: of \: x \: for \: which \: {x}^{2} - 8x + 12 = 0$

$i.e.,(x - 6)(x - 2) = 0 \rightarrow x = 6,2 \\ \therefore domain \: of \: f(x)$

= R-{2,6}