First slide

Continuity

Question

$The values of x where the function f (x) = \frac{\tan x \log (x - 2)}{x^{2} - 4 x + 3} is discontinuous are given by$

Moderate

A

$(- \infty, 2)$
B

$(- \infty, 2) \cup \{3\}$
C

$(- \infty, 2) \cup {3, n π + π / 2 : n \geq 1}$
D

None of these

Solution

$f (x) = \frac{\tan x \log (x - 2)}{x^{2} - 4 x + 3}, being product and quotient of functions \tan x$
$\log (x - 2) and (x^{2} - 4 x + 3) must be continuous in its domain of definition.$
$\tan x is discontinuous in {(2 n + 1) π / 2 : n \in Z}$
$\log (x - 2) discontinuous for x \leq 2$
$and x^{2} - 4 x + 3 = 0 for x = 1 and 3 .$
$Hence f (x) is discontinuous in [- \infty, 2] \cup {3, n π + π / 2 : n \in Z}$
$[- \infty, 2] \cup {3, n π + π / 2 : n \geq 1}$
Hence (3) is the correct answer.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App