Find the domain of f(x)= 10 (x^2-5 x+6 ) - Vidyadip

Question

Find the domain of

$f(x)=\log 10\left(x^2-5 x+6\right)$

✓

Answer

$f(x)=\log _{10}\left(x^2-5 x+6\right)$
$
x^2-5 x+6=(x-2)(x-3)
$
$f$ is defined, when $(x-2)(x-3)>0$
$
\therefore x <2 \text { or } x >3
$
Solution of $(x-a)(x-b)>0$ is $x<a$ or $x>b$ where $a<b$
$\therefore$ Domain of $f=(-\infty, 2) \cup(3, \infty)$

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