If function `f(x)=sqrt2` when `x in Q` and `0` when `x !in Q` then `(fof)sqrt4=`

Let R and Q be the sets of real numbers and rational numbers respectively.If a in Q and fR rarr R is defined by,f(x)=x when x in Q,a-x when x not in Q then show that fof (x)=x for all x in R

If f : R -> R be a function such that f(x) = { x|x| -4; x in Q, x|x| - sqrt3; x !in Q then f(x) is

The function f(x)={{:( 1, x in Q),(0, x notin Q):} , is

The function f(x)={{:( 1, x in Q),(0, x notin Q):} , is

If f(x)=sqrt(1+x)-3sqrt(4-x) , then f(x) is defined when x lies in

If a function f(x) is such that f(x+1/x) = x^(2)+1/(x^2) , then (fof)(sqrt(11)) =

Let, the function f:RRrarrRR be defined by, f(x)={:{(1 ,"when " x in QQ),(-1,"when "x !in QQ):}" Find" f(2),f(sqrt(2)),f(pi),f(2.23),f(e)

If f(x) = 0 when x is an integer. = 2 when x is not an integer, then find - (a) f(0), (b) f(sqrt2) .

If the function f(x)=sqrt(2x-3) is invertible then, find its inverse. Hence prove that (fof^(-1)) (x)=x .