Question

Find the domain of the function:

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

Answer 1

Here $f\left(x\right)=\frac{x^2+2x+1}{x^2-8x+12}.$

f(x) is a rational function of x.

f(x) assumes real values of all x except for those values of x for which

$x^2-8x+12=0$

$\Rightarrow (x-6)(x-2)=0$

$\Rightarrow$ $x=2,6.$

$\therefore$ Domain of function = R - {2, 6}