Question

The domain of the function $f\left(x\right)=\frac{x^2+1}{x^2-3x+2}$ is __________ .

Answer 1

f(x) = $\frac{x^2+1}{x^2-3x+2}$
f(x) is defined if x² − 3x + 2 ≠ 0
i.e f(x) is not defined
for x² − 3x + 2 = 0
i.e x² − 2x − x + 2 = 0
(x² − 2x) −1 (x − 2) = 0
x (x − 2) −1 (x − 2) = 0
i.e (x − 1) (x − 2) = 0
i.e x = 1 or x = 2
i.e for x = 1 or x = 2, f (x) is not defined
∴ Domain of f(x) = R ~ {1,2}