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

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

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

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

If the functions f(x)a n dg(x) are defined on R rarr R such that f(x)={0, x in r a t ion a l x ,x in i r r a t ion a l a n dg(x)={O , x in i r r a t ion a l x ,x in r a t ion a l then (f-g)(x)i s (a)one-one and onto (b)neither one-one nor onto (c)one-one but not onto (d)onto but not one-one

Let f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l has exactly two points of continuity then the value of b are (0,3] b. [0,1] c. (0,2] d.varphi

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

Find the derivative of (log x)^(cos x) w.r.t.x

If f(x)={(x-4)/(|x-4|a+b ,ifx=4)+a ,ifx 4i scon t inuou sa tx=4,fin da , b