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

Jun 27, 2018

None

#### Explanation:

This function is continous. In fact, $f \left(x\right) = | x |$ is a continuous function, and $g \left(x\right) = | x + 1 |$ is simply $f \left(x + 1\right)$, 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.

Jun 27, 2018

The function is continuous but not differentible at $\left(- 1 , 1\right)$ and $\left(0 , - 1\right)$

#### Explanation:

The function is $f \left(x\right) = | x | - | + 1 |$

The changing values occur when

$x = 0$ and $x + 1 = 0$

Therefore,

In the interval $\left(- \infty , - 1\right)$,

$f \left(x\right) = - x - \left(- x - 1\right) = 1$

In the interval $\left(- 1 , 0\right)$,

$f \left(x\right) = - x - \left(x + 1\right) = - 2 x - 1$

In the interval $\left(0 , + \infty\right)$,

$f \left(x\right) = x - \left(x + 1\right) = - 1$

The function is continuous but not differentiable at $\left(- 1 , 1\right)$ and $\left(0 , - 1\right)$

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