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

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 f(x)=|x| at 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

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

Discuss the surjectivity of the following functions: f:R rarr given by f(x)=x^(3)+2 for all x in R

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

f(x)= maximum (sin t,0<=t<=x),0<=x<=2 pi discuss the continuity of this function at x=(pi)/(2)f(x)= maximum (sin t,0<=t<=x),0<=x<=2 pi

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.

Let f(x)=x^(3)-x^(2)-x+1 and g(x)={max{f(t);0<=t<=x},0<=x<=1,3-x,1<=x<=2 Discuss the continuity and differentiability of the function g(x) in the interval (0,2).