Discuss the continuity of the following function : `f(x)={1,ifxi sr a t ion a l0,ifxi si r r a t ion a l`

Discuss the continuity of the following function f(x)={1,\ if\ x\ i s\ r a t ion a l , 0\ if\ x\ i s\ irrational

Which of the following function is/are periodic? (a)f(x)={1,xi sr a t ion a l0,xi si r r a t ion a l (b)f(x)={x-[x]; 2n

Discuss the continuity of f(x)={x^2,xi sr a t ion a l-x^2,xi si r r a t ion a ldot

Discuss the continuity of the function f given by f(x) = |x| a t x = 0 .

Let f(x)=("lim")_(nvecoo){("lim")_(nvecoo)cos^(2m)(n !pix)}, where x in Rdot Then prove that f(x)={1,ifxi sr a t ion a l0,ifxi si r r a t ion a l

Column I: Function, Column II: Type of function f(x)="{"sgnx")"^(sgn)}; x!=0,n is an odd integer, p. odd function f(x)=x/(e^x-1)+x/2+1 , q. even function f(x)={0,ifxi sr a t ion a l1,ifxi si r r a t ion a l , r. neither odd nor even function. f(x)=max{tanx ,cotx} , s. periodic

Column I: Function, Column II: Type of function f(x)="{"sgnx")"^(sgn)}; x!=0,n is an odd integer, p. odd function f(x)=x/(e^x-1)+x/2+1 , q. even function f(x)={0,ifxi sr a t ion a l1,ifxi si r r a t ion a l , r. neither odd nor even function. f(x)=max{tanx ,cotx} , s. periodic

Find the value of x where f(x)={x ,ifxi sr a t ion a l1-x ,ifxi si r r a t ion a li scon t inuou sdot

Find the value of x where f(x)={x ,ifxi sr a t ion a l1-x ,ifxi si r r a t ion a li scon t inuou sdot

Find the value of x where f(x)={x ,ifxi sr a t ion a l1-x ,ifxi si r r a t ion a li scon t inuou sdot