Find the Domain of \(f(x)=\dfrac{x^2+1}{x^2-3x+2}\)

Solution

Given

\[ f(x)=\frac{x^2+1}{x^2-3x+2} \]

For a rational function, the denominator must not be zero.

Therefore,

\[ x^2-3x+2\ne0 \]

Factorize the denominator:

\[ x^2-3x+2=(x-1)(x-2) \]

Hence,

\[ (x-1)(x-2)\ne0 \]

Therefore,

\[ x\ne1 \quad \text{and} \quad x\ne2 \]

So all real numbers except \(1\) and \(2\) belong to the domain.