is the function defined by f(x)= IxI a continous function ??? pls explain in detail as i am very bad in thinking steps

Asked by rahmanafeef | 7th Apr, 2020, 11:32: PM

Expert Answer:

To check the continuity of f(x)=|x|
f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell x comma space space space space space space x greater or equal than 0 end cell row cell negative x comma space space space x less than 0 end cell end table close
W e space o n l y space n e e d space t o space c h e c k space t h e space c o n t i n u i t y space o f space f space a t space x equals 0
L H L equals limit as x rightwards arrow 0 to the power of minus of f left parenthesis x right parenthesis equals limit as x rightwards arrow 0 of space minus x equals 0
R H L equals limit as x rightwards arrow 0 to the power of plus of f left parenthesis x right parenthesis equals limit as x rightwards arrow 0 of space x equals 0
rightwards double arrow L H L equals R H L equals f left parenthesis 0 right parenthesis
T h u s comma space f space i s space c o n t i n u o u s space a t space x equals 0
H e n c e comma space f left parenthesis x right parenthesis equals vertical line x vertical line space i s space c o n t i n u o u s space f o r space a l l space x element of R.

Answered by Renu Varma | 8th Apr, 2020, 10:39: AM