Let `f:[a,b]rarrR` be any function which is such that f(x) is rational for inrrational x and f(x) is irrational for rational x, Then in [a, b]

Let f : [a,b]-> R be any function which is such that f(x) is rational for irrational x and that f(x) is iirrational for rational x, then in [a,b]

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

Discuss the continuity of f(x)={x^2, x is rational -x^2, x is irrational dot

if (log)_a x=b for permissible values of a and x then identify the statements which can be correct. (a) If a and b are two irrational numbers then x can be rational (b) if a is rational and b is irrational, then x can be rational (c) if a is irrational and b is rational, then x can be rational (d) If a and b are two rational numbers then x can be rational .

If f(x)={(sin x;x rational) (cos x;x is irrational) then the function is

Let f(x) be a function such that f(x), f'(x) and f''(x) are in G.P., then function f(x) is

If (log)_a x=b for permissible values of a and x , then identify the statement(s) which can be correct. (a)If a and b are two irrational numbers, then x can be rational. (b)If a is rational and b is irrational, then x can be rational. (c)If a is irrational and b is rational, then x can be rational. (d)if aa n d b are rational, then x can be rational.

Let f(x) be a function such that f'(a) ne 0 . Then , at x=a, f(x)

Let f be a function from a set X to X, such that (f(f(x)) = x, for all x in X , then