Question

, ifx<09.-1, if x20

Answer 1

The given function is,

f( x )={ x | x |   ,  x<0 −1  ,  x≥0

Simplify the given function,

f( x )={ x −x =−1  ,  x<0 −1          ,  x≥0

The function becomes f( x )=−1  ,  ∀x∈R.

The limit of the function for a real number k is,

limf( x ) x→k =f( −1 ) =−1

The function is continuous for all real numbers. Therefore, there is no point of discontinuity for the given function.