Question

*f(x) = | x – 5 | is ​

Answer 1

Answer:

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Answer 2

We know that the greatest integer function is discontinuous at integer values. For a value of x just smaller than 5, the greatest integer smaller than it is 4. So,

limx→5−[x]=4

f(x=5)=[5]=5

For a value of x just bigger than 5, the greatest integer smaller than it is 5. So,

limx→5+[x]=5

Since limx→5−f(x)=f(5), the function is not left continuous.

Since limx→5+f(x)=f(5), the function is right continuous.