Given:
[tex]g(x)=\frac{17x-1}{x^2-4x+3}[/tex]
The domain of the function is a set of all input values for which the function is real or defined.
[tex]\begin{gathered} \text{The function is not defined when }x^2-4x+3=0 \\ x^2-4x+3=0 \\ x^2-x-3x+3=0 \\ x(x-1)-3(x-1)=0 \\ (x-1)(x-3)=0 \\ \Rightarrow x=1,3 \end{gathered}[/tex]
The function is defined for real x except x = 1 ,3.
The domain of the function is x < 1 or 1 < x < 3 or x > 3
[tex]\begin{gathered} x<1\text{ or 1}3 \\ (-\infty\: ,\: 1)\cup(1,\: 3)\cup(3,\: \infty) \end{gathered}[/tex]
