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

Find the value of x where f(x)={x ,if x is rational 1-x ,if x is irrational is continuous dot

If the functions f(x)a n dg(x) are defined on R rarr R such that f(x)={(0, x in rational) (x ,x in irrational) and g(x)={(O, x in irrational x), (x in rational) 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

A function is defined as, f(x)={(0, where x is rational),(1, where x is irrational)}: . Then f(x) is

If f(x) = 2x + 3, then x is rational. =x^(2)+1 , when x is irrational. then find - (a) f(0), (b) f(pi) .

IF f(x)={{:(x,"if",x,"is rational"),(1-x,"if",x, "is irrational"):},"then find" lim_(xto1//2) f(x) if exists.

Let f:RrarrR be defined as . f(x)={(0, "x is irrational"),(sin|x|,"x is irrational"):} Then which of the following is true?

Two mappings f:R to R and g:R to R are defined as follows: f(x)={(0,"when x is rational"),(1,"when x is irrational"):} and g(x)={(-1,"wnen x is rational"),(0,"when x is irrational"):} then the value of [(gof)(e)+(fog)(pi)] is -

Let f(x)={(-1+sinK_1pix, x is rational), (1+cosK_2pix, x is irrational) :} If f(x) is periodic function, then:

Let f: R to R be defined as f(x)={{:(0", x is irrational"),(sin|x|", x is rational"):} Then which of the following is true?

Which of the following function is/are periodic? A. f(x)={1,0,x is rationalx is irrational B. f(x)={x−[x],12,2n≤x<2n+12n+1≤x<2n+2 where [.] denotes the greatest integer function n∈Z C. f(x)=(−1)[2xπ, where [.] denotes the greatest integer function D. f(x)=x−[x+3]+tan(πx2), where [.] denotes the greatest integer function, and a is a rational number