Let `ZZ` be the set of integers and f be a subset of `ZZxxZZ`, such that,
`f={(xy,x +y):x,y in ZZ}`
Is f a function from `ZZ " into "ZZ` ? Give reasons for your answer.

Let f be a subset of ZZ xxZZ such that f={(xy,x-y):x, y in ZZ} Is f a mapping from ZZ "into" ZZ . Give reasons for your answer.

Let f be the subset of Z xx Z defined by f={(ab,a+b) : a,b in Z} . Is f a function from Z to Z? Justify your answer.

Let ZZ be the set of integers and f:ZZ rarr ZZ be defined by , f(x)=x^(2) . Find f^(-1) (16) and f^(-1) (-4)

Let ZZ be the set of integers and A={x:x =6n, n in ZZ},B={x : x =4n,n in ZZ}, find A capB.

If ZZ be the set of integers, prove that the function f: ZZ rarrZZ defined by f(x)=|x| , for all x in Z is a many -one function.

Let ZZ be the set of integers and let R be the relation on ZZ defined as R={(x,y)|x,y in ZZ and x^2+y^2=100} Find R as the set of ordered pairs. Also find its domain and range.

Let IR be the set of real numbers andf : IR be such that for all x, y in IR |f(x)-f(y)le|x-y|^3 Prove that f is a constant function.

Let ZZ be that set of integers and f:ZZ rarr ZZ be defined by f(x)=2x, for all x in ZZ and g: ZZ rarr ZZ be defined by, (for all x in ZZ) g(x)={((x)/(2) " when x is even" ),(0" when x is odd" ):} Show that, (g o f) =I_(ZZ) , but (f o g) ne I_(ZZ) .

Let ZZ be the set of integers and the mapping f: ZZ rarr ZZ be defined by, f(x)=x^(2) . State which of the following is equal to f^(-1) (4) ?

Let RR be the set of real numbers and f: RR rarr RR be such that for all x,y inR , |f(x)-f(y)|^2le (x-y)^3 Prove that f is a constant function.