Question

Find the domain of the following real function:

f(x)= $\frac{2x-3}{x^2-3x+2}$

Answer 1

Given ,

The function is f(x) = $\frac{2x-3}{x^2-3x+2}$

We know that ,

For function to be real , we must have

Denominator ≠ 0

Thus ,

$\sf \Rightarrow {(x)}^{2} - 3x + 2 ≠ 0 \\ \\ \sf \Rightarrow</p><p> {(x)}^{2} -1x - 2x + 2 ≠ 0 \\ \\ \sf \Rightarrow</p><p>x(x - 1) - 2(x - 1) ≠ 0 \\ \\\sf \Rightarrow </p><p>(x -2) ≠ 0 \: \: and \: \: (x- 1) ≠ 0 \\ \\ \sf \Rightarrow</p><p>x ≠2 \: \: and \: x ≠1$

$\therefore \bold{ \underline{ \sf Domain \: of \: f(x) = R - \{2,1 \}}}$