Find the domain of the function $f(x)= rac{x^{2}+2 x+1}{x^{2}-8 x+12}$


Find the domain of the function $f(x)=\frac{x^{2}+2 x+1}{x^{2}-8 x+12}$


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

$f(x)=\frac{x^{2}+2 x+1}{x^{2}-8 x+12}=\frac{x^{2}+2 x+1}{(x-6)(x-2)}$

It can be seen that function f is defined for all real numbers except at x = 6 and x = 2.

Hence, the domain of $f$ is $\mathbf{R}-\{2,6\}$.

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