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`

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

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

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

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

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)={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 surjectivity of f:R rarr R given by f(x)=x^(2)+2 for all x in R

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