Question

Calculate the discontinuity of f(x) = X / |X|

Answer 1

In the question, we are asked to find the discontinuity of the function below;

`f(x)=(x)/(|x|)`

Step-by-step explanation

The discontinuity of a function is the point at which the function becomes undefined, or occurs at values of x where the graph can't be evaluated. This can be gotten by equating the denominator to zero and solving.

`\mleft|x\mright|=0`

Using the absolute rule

`\mathrm{If}\: |u|\: =\: 0\: \mathrm{then}\: u\: =\: 0`

Hence,

`If\text{ }\mleft|x\mright|=0\text{ }\therefore\text{ }x=0`

Answer

We can therefore conclude that the discontinuity occurs at x = 0