Question

The values of $x$ for which the function $f\left(x\right)=\frac{x^2+x+1}{x^2-7x+12}$ is not defined, is

• A. $\{3,4\}$
• B. $\{3,-4\}$
• C. $\{-3,-4\}$
• D. the function is defined everywhere

Answer 1

The correct option is A $\{3,4\}$

$f\left(x\right)=\frac{x^2+x+1}{x^2-7x+12}$
It is a rational function, so the function is not defined when the denominator is equal to zero.
$x^2-7x+12=0\Rightarrow (x-3)(x-4)=0\Rightarrow x=3,4$