# question on continuityf(x)=x^2, x belongs to set of integers onlyf(x)=k(x^2-4)/2-x, x does not belong to set of integers.find value of k so that f(x) is continuous.   plz help

Jitender Singh IIT Delhi
8 years ago
Ans:
$f(x) = x^{2}, x = I$
$f(x) = \frac{-k(x^{2}-4)}{2-x}, x \neq I$
$f(x) = -k(x+2), x \neq I$
For function to be continuous
$\lim_{h\rightarrow 0}f(I-h) = I^{2} = \lim_{h\rightarrow 0}f(I+h)$
$\lim_{h\rightarrow 0}-k(2+I-h) = I^{2} = \lim_{h\rightarrow 0}-k(2+I+h)$
$k = \frac{-I^{2}}{I+2}$
I = Integer
Cheers!
Thanks & Regards
Jitender Singh
IIT Delhi