Could someone please check my work

Ler fil - RR and define | fliR - RR by If1 (x) = / f(x)/. If Iflis continuous aT C, does it follow That f is continuous at C? If | f (x)| is always positive real number, say 1 and c is an accumulation point of all X, Then f( x ) 1 = 1 , which means of( x ) = 1 for some values of X > C and f( x) =- 1 for All Other values of XEC. So,. .. There is no single value of x for which of ( x . ) = f ( x 2 ), which implies xitx2 by injection. Since f( x ). Cannot have Two limits, - I and I, Then The continuity of If(x)I does not imply The Continuity of f (x)