Question

Find the domain of the function f(x)=(x²+2x+3)/(x²-8x+12)

Answer 1

f(x)=x²+2x+3/(x²-8x+12)
x²-8x+12 =0
x²-6x-2x+12=0
x(x-6)-2(x-6)=0
(x-6)(x-2)=0
if x-6=0
x=6
if x-2=0
x=2
so domain=R-{6,2}

PLEASE SELECT MY ANSWERS AS BRAINLIEST

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}