Letf:N→N be defined by fx=x2+x+1,  x∈N. Then f is

Let x,y∈N  such that  fx=fy.fx=fyor x2+x+1=y2+y+1or x-yx+y+1=0i.e. x=y  or  x=-y-1∉NTherefore, f is one-one.Also, f(x) does not take all positive integral values.so not ontoHence, f is into.