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 f(x)={{:("0, when x is an integer ,"),("2, when x is not an integer,"):} then f(pi) =

The polynomial f(x) is defined by f(x)={{:("0 when x is an integer ,"),("1 when x is not an integer ,"):} Then compute : (a)f(-2),(b)f(sqrt3) .

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

A function f(x) is defined as follows: f(x)={:{(1",","when x is an integer"),(0",","when x is not an integer"):} Draw the graph of the function and from the graph find its points of discontinuity (if any).

If f(x) = x when 0lexlt1 = 2 - x when 1lexle2 = x-x^(2)/2 when xgt2 , then f(1.5) =

Let f(x) = Ax^2+Bx+C where A,B,C are real numbers. Prove that if f(x) is an integer whenever x is an integer, then the number 2A, A+B and C are all integers. Conversely, prove that if the numbers 2A, A+B and C are all integer then f(x) is an integer whenever x is an integer.

If f(x)={{:("2x+3, when x is an rational ,"),(x^(2)+1", when x is irrational,"):} then f(0) =

Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C are real numbers. Prove that if f(x) is an integer whenever x is an integer, then the numbers 2A ,A+B ,a n dC are all integer. Conversely, prove that if the number 2A ,A+B ,a n dC are all integers, then f(x) is an integer whenever x is integer.

If f(x) = (p - x^n)^(1/n), p gt 0 and n is positive integer, then the value of f[f(x)]

Let f(x)=Ax^2+Bx+C where A, B, C are three real constants, if f(x) is integer for integral values of x, then prove that each of 2A, (A+B) and C is an integer. Conversely, if each of 2A, (A+B) , C is an integer then f(x) will be integer for integral values of x.