Question

The value of 'x' for which f(x)=|x| - |x+1| is discontinuos is ?

Answer 1

None

Explanation:

This function is continous. In fact, `f(x)=|x|` is a continuous function, and `g(x)=|x+1|` is simply `f(x+1)`, which means that it is a translated version of `f`, and thus is still continuous.

Finally, the sum (or difference) of continuous functions is still continuous.

Answer 2

The function is continuous but not differentible at `(-1,1)` and `(0,-1)`

Explanation:

The function is `f(x)=|x|-|+1|`

The changing values occur when

`x=0` and `x+1=0`

Therefore,

In the interval `(-oo, -1)`,

`f(x)=-x-(-x-1)=1`

In the interval `(-1, 0)`,

`f(x)=-x-(x+1)=-2x-1`

In the interval `( 0, +oo)`,

`f(x)=x-(x+1)=-1`

The function is continuous but not differentiable at `(-1,1)` and `(0,-1)`

graph{|x|-|x+1| [-5.55, 5.55, -2.773, 2.776]}