Limits Continuity And Differentiability Question 23
Question: If $ y=\frac{1}{t^{2}+t-2} $ where $ t=\frac{1}{x-1} $ , then find the number of points of discontinuities of $ y=f(x), $ ,
Options:
A) 1
B) 2
C) 3
D) 4
Show Answer
Answer:
Correct Answer: C
Solution:
$ t=\frac{1}{x-1} $ is discontinuous at $ x=1. $ Also $ y=\frac{1}{t^{2}+t-2} $ discontinuous at $ t=-2 $ and $ t=1 $
When $ t=-2,\frac{1}{x-1}=-2\Rightarrow x=\frac{1}{2} $
When $ t=1,\frac{1}{x-1}\Rightarrow x=2 $ So, $ y=f(x) $ is discontinuous at three points $ x=1,\frac{1}{2},2 $
BETA
