If `f: RR rarr RR`, `f(x) = {(1,; "when"\ x in QQ), (-1,;"when"\ x notin QQ):}` then image set of `RR` under `f` is

If f: R rarr R, f(x) ={(1,; "when " x in QQ), (-1,; "when " x !in QQ):} then image set of RR under f is

Let RR and QQ be the sets of real numbers and rational numbers respectively. If a in QQ and f: RR rarr RR is defined by , f(x)={(x " when" x in QQ ),(a-x" when " x notin QQ ):} then show that , (f o f ) (x) = x , for all x in RR

Let, the function f:RRrarrRR be defined by, f(x)={:{(1 ,"when " x in QQ),(-1,"when "x !in QQ):}" find" pre-image of 1 and (-1)

If the function f: RR rarr RR be defined by, f(x)={(x " when "x in QQ ),(1-x " when " x in QQ ):} then prove that , (f o f)=I_(RR) .

Let, the function f:RRrarrRR be defined by, f(x)={:{(1 ,"when " x in QQ),(-1,"when "x !in QQ):}" find" range of f

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)

Let f: RR rarr RR be defined by f(x)={(|x|/(x) " when " x ne 0 ),(0" when "x =0 ):} and the function g: RR rarr RR be defined by g(x) =[x] where [x] is the greatest integer function. Prove that the functions (f o g) and (g o f) are same in [-1,0).

Let RR and QQ be the set of real numbers and rational numbers respectively and f:RR to RR be defined as follows: f(x)={:{(5",", "when "x in QQ),(-5","," when " x !in QQ):} Find f(3),f(sqrt(3)),f(3.6),f(pi),f(e) and f(3.36),

Let RR be the set of real numbers and f, Rrto RR be defined by f (x)= cos ec x(x ne npi, n in z): then image set of f is-