Let NN be the set of natural number and `f: NN -{1} rarr NN ` be defined by:
`f(n)`= the highest prime factror of n .
Show that f is a many -one into mapping

let NN be the set of natural numbers and f: NN uu {0} rarr NN uu [0] be definedby : f(n)={(n+1 " when n is even" ),(n-1" when n is odd " ):} Show that ,f is a bijective mapping . Also that f^(-1)=f

Let RR be the set of real numbers and f: RR rarr RR be defined by , f(x) =x^(3) +1 , find f^(-1)(x)

Let A={9,10,11,12,13} and let f: A to N be defined by f(n)= the highest prime factor of n. Find the range of f.

Let RR be the set of real number and f: RR rarr RR , be given by f(x)=2x^(2)-1 . .Is this mapping one -one ?

Let RR be the set of real numbers and f:RR rarr RR be defined by , f(x)=2x +1 . Find g: RR rarr RR , such that (g o f) (x) =10 x+10

Let RR be the set of real numbers and the mapping f: RR rarr RR be defined by f(x)=2x^(2) , then f^(-1) (32)=

If NN be the set natural numbers, then prove that, the mapping f: NN rarr NN defined by , f(n) =n-(-1)^(n) is a bijection.

If NN be the set of nature numbers and N_(a) ={an , n in NN}, then N_(5) nnN_(7) is-

Let RR^(+) be the set of positive real numbers and f: RR rarr RR ^(+) be defined by f(x) =e^(x) . Show that, f is bijective and hence find f^(-1)(x)

Let RR be the set of real numbers and f, Rrto RR be defined by f (x)= cos ec x(x ne npi, n in z): then image set of f is-