Limits Continuity And Differentiability Question 81
Question: If $ f(x)= \begin{cases} x^{2}-ax+3,x is rational \\ 2-x,x is irrational \\ \end{cases} . $ is continuous at exactly two points, then the possible values of a are
Options:
A) $ (2,\infty ) $
B) $ (-\infty ,3) $
C) $ (-\infty ,-3)\cup (3,\infty ) $
D) none of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x)= \begin{cases} x^{2}-ax+3, \\ 2-x, \\ \end{cases} .\begin{vmatrix} xisrational \\ xisirrational \\ \end{vmatrix} $
It is continuous when $ x^{2}-ax+3=2-x $ or $ x^{2}-(a-1)x+1=0 $
Which must have two distinct roots for $ {{(a-1)}^{2}}-4>0 $
or $ (a-1-2)(a-1+2)>0 $
or $ a\in (-\infty ,-1)\cup (3,\infty ) $
BETA
