2). If f:R→S defined by f(x)=sinx−3–√cosx+1f(x)=sinx-3cosx+1 is onto , then the interval of S is :

3). Prove that the function F:NN→, defined by f(x)=x2+x+1f(x)=x2+x+1 is 

a). One-one onto 

b). Many-one onto 

c). One-one but not onto 

d). None of these

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Show that the function f: N→ Z, defined by (n-1), when n is odd f(n) = 2 1 -n, when n is even 2 is both one-one and onto. Show that the function f: N→ Z, defined by (n-1), when n is odd f(n) = 2 1 -n, when n is even 2 is both one-one and onto.