Chapter 7 - Functions - Exercise Set 7.2 - Page 414: 9

$ f:X\rightarrow Y \\ f(1)=1,f(2)=2,f(3)=3\\ b-\\ g:X\rightarrow Z\\ g(1)=1,g(2)=1,g(3)=2\\ c-\\ h:X\rightarrow X\\ h(1)=2,h(2)=2,h(3)=2\\ d-\\ k:X\rightarrow X\\ k(1)=3,k(2)=2,k(3)=1\\ $

$X=\left \{ 1,2,3 \right \},Y=\left \{ 1,2,3,4 \right \},Z=\left \{ 1,2 \right \}\\ a-\\ f:X\rightarrow Y \\ f(1)=1,f(2)=2,f(3)=3\\ it\,is\,clear\,that\,f\,\,is\,one-to-one\\ f\,\,is\,not\,onto\,as\,\\ 4\in Y\,is\,not\,image\,of\,some\,element\,in\,X \\ b-\\ g:X\rightarrow Z\\ g(1)=1,g(2)=1,g(3)=2\\ because\,g(1)=g(2)=1\,and\,1\neq 2 \\ so\,g\,is\,not\,one-to-one\\ g\,is\,onto\,as\,\,1,2(elements\,\,of\,\,Z)is\,\,image\,of\,some\,element\,in\,X\\ c-\\ h:X\rightarrow X\\ h(1)=2,h(2)=2,h(3)=2\\ because\,h(1)=h(2)=h(3)=2\,and\,1\neq 2\neq 3 \\ so\,h\,is\,not\,one-to-one\\ and\,1,3\,\,is\,not\,image\,of\,some\,element\,in\,X\\ so\,h\,is\,not\,onto \\ d-\\ k:X\rightarrow X\\ k(1)=3,k(2)=2,k(3)=1\\ k\,is\,one-to-one\\ k\,is\,onto\\ k\,is\,onto\,as\,\,1,2,3(elements\,\,of\,\,X)is\,\,image\,of\,some\,element\,in\,X\\ $