If f(x) =x when `x in Q` and -x when `x not in Q` (A)Allrational numbers (C) Zero and 1 only (B) Zero only (D) No where

If function f(x)=sqrt(2) when x in Q and 0 when x!in Q then (fof)sqrt(4)=

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(x)=(|x|)/(x) and c be a non-zero real number, show that |f(c)-f(-c)|=2.

When f(x) is divided by (x-2) , the qoutient is Q (x) and the remainder is zero . And when f(x) is divided by [Q(x)-1] , the qoutient is (x-2) and the remainder is R (x) . Find the remainder R (x).

If f(2x+y/8,2x-y/8)=x y , then f(m , n)+f(n,m)=0 (a) only when m=n (b) only when m!=n (c) only when m=-n (d) for all m and n

If f(2x+y/8,2x-y/8)=x y , then f(m , n)+f(n,m)=0 (a) only when m=n (b) only when m!=n (c) only when m=-n (d) for all m and n

If f(2x+y/8,2x-y/8)=x y , then f(m , n)+f(n,m)=0 (a) only when m=n (b) only when m!=n (c) only when m=-n (d) for all m and n

If f(x) is a twice differentiable function such that f(a)=0, f(b)=2, f(c)=-1,f(d)=2, f(e)=0 where a < b < c < d e, then the minimum number of zeroes of g(x) = f'(x)^2+f''(x)f(x) in the interval [a, e] is