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 ,\ if\ x\ r a t ion a l1-x ,\ if\ x\ i s\ irrational\ is\ contiuous.

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

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

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,ifxi sr a t ion a l0,ifxi si r r a t ion a l

"I f"f(x)={x^3-6x^2; ifxi sr a t ion a l-11 x+6;ifxi si r r a t ion a l"t h e n" f(x) is continuous for all real x f(x) is continuous at x=1,2,3. f(x) is discontinuous at infinite points f(x) discontinuous for all real xdot

Statement 1: If f(x)={x ,\ if\ x\ i s\ irr a t ion a l1-x ,\ if\ x\ i s\ r a t ion a l\ ,\ t h e n(lim)_(x->1//2)f(x) does not exist. Statement 2: x->1/2 can be rational or irrational value. Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true; Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

If f(x)={x ,xi sr a t ion a l1-x ,xi si r r a t ion a l ,t h e nf(f(x)) is xAAx in R (b) {x , xi si r r a t ion a l1-x ,xi sr a t ion a l {x ,xi sr a t ion a l1-x ,xi si r r a t ion a l (d) none of these

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