Math Help - continuity

1. continuity

discuss the continuity of function f(x)=(3*x-mod(x))/5*x) x(not equal)=0
=4 x=0

i think function is discontinuous at x=0

2. Re: continuity

Express $f(x)=\begin{Bmatrix}{ 2/5}&\mbox{ if }& x>0 \\4 & \mbox{if}& x=0\\ 4/5 & \mbox{if}& x<0\end{matrix}$

Conclude.

3. Re: continuity

Originally Posted by prasum
discuss the continuity of function f(x)=(3*x-mod(x))/5*x) x(not equal)=0
=4 x=0

i think function is discontinuous at x=0
Is...

$\lim_{x \rightarrow 0+} f(x) = \frac{2}{5}$

$\lim_{x \rightarrow 0-} f(x) = \frac{4}{5}$

... so that, independently from the value of f(x) in x=0, only one conclusion is possible...