The function `f(x)={0, x` is irrational and `1, x` is rational, is

Discuss the continuity of the following function : f(x)={1,if x is rational , 0 ,if x is irrational

Show that the function f(x)={{:(1,if x is "rational"),(-1, if x is "rational"):} (Dirichlet’s function ) is discontinuous every where.

Let f(x)=[0, if x is rational and x if x is irrational and g(x)=[0, if x is irrational and x if x is rational then the function (f-g)x is

Let f(x)=0 for x is rational and x if x is irrational and g(x)=0 if x is irrational and x if x is rational then the function (f-g)x is

Show that the function f:R rarr R:f(x)={1 if x is rational and -1, if x is irrational is many- one into

If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, when x is rational and x, when x is irrational then (f-g) is

If the functions f(x) and g(x) are defined on R -> R such that f(x)={0, x in retional and x, x in irrational ; g(x)={0, x in irratinal and x,x in rational then (f-g)(x) is

If f(x)={x,x is rational 1-x,x is irrational , then f(f(x)) is

The functions RR,g:R R are defined as f(x)={0, whenxis rational and 1 when x is irrational } and g(x)={-1 when x is rational and 0 when x~ is~ irrational}~ find~ fog (pi) and gof(e)