Define `f:Z rarrZ` by `f(x)={{:(x//2,"(x is even)"),(0,"(x is odd)"):}` then f is

Let z denote the set of all integers.Define : f:z rarr z by f(x)={(x)/(2),(xiseven),0,(xisodd) Then f is

If function f:ZtoZ is defined by f(x)={{:((x)/(2), "if x is even"),(0," if x is odd"):} , then f is

Let Z denote the set of all integers and f: Z to Z defined by f(x) = {{:(x+2, ("x is even")),(0, ("x is odd")):} , Then f is:

Let f : Z to Z be given by f(x) = {((x)/(2) if"is even"),(0 if" is odd"):} Then f is

On the set of integers Z, define f : Z to Z as f(n)={{:((n)/(2)",",,"n is even."),(0",",,"n is odd."):} Then, f is

Let f(x)={((x-1,"x is even")),("2x, x is odd"):}, "x"inN be a function and f(f(f(a))))=21 then lim_(xtoa)(abs(x^3)/a-[x/a])=

A function f: Z rarrrZ is defined as below f(x) = {:{(x+3, if x is odd),(x/2, if x is even):} , If k is an odd integer and f(f(k+3) = 27 , then the sum of the digits of the number k equals.

f: Z rarrZ and g : Z rarrZ are defined as follow : f(n) ={:{(n+2," n even"),(2n-1," n odd"):}, g(n) ={{:(2n,"n even"),((n-1)/2,"n odd"):} Find fog and gof.

Prove that int_(-a)^(a) dx = {(2int_(0)^(a) f(x) dx, if f(x) "is even"),(0, if f(x) "is odd"):} and hence evaluate (b) int_(-pi//2)^(pi//2) sin^(7) x dx .

Let f:N to Z and f (x)=[{:((x-1)/(2),"when x is odd"),(-(x)/(2),"when x is even"):}, then: