First slide

Functions (XII)

Question

$The domain of f (x) = \frac{1}{\sqrt{(x - 1) (x - 2) (1 - 2 x)}} is$

Moderate

A

$(- \infty, \frac{1}{2}) \cup (1, 2)$
B

$(1, 2)$
C

$(- 1, \infty)$
D

$R - (1, 2)$

Solution

$T h e d o m i a n o f t h e f u n c i t o n i s t h e s e t o f a l l r e a l n u m b e r s f o r w h i c h (x - 1) (x - 2) (2 x - 1) > 0$
$T h e g r a p h o f a b o v e f u n c t i o n i n t e r s e c t x - a x i s a t x = 1, 2, \frac{1}{2}$
Use the sign changes on the number line, we can decide where the function is positve
$H e n c e, t h e d o m a i n i s (- \infty, \frac{1}{2}) \cup (1.2)$

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