Question

Example 12 Show that f: NŐN, given by
(x+1, ifx is odd,
(x-1, if x is even
is both one-one and onto.​

Answer 1

Answer:

x1+1=x2+1,x1-1=x2-1

x1=x2,x1=x2

is One One

f(x)=x+1

f(x)=y

f^-1(y)=x

x+1=y

x=y-1 sub in f(x)

f^-1(y)=y-1+1=y

is onto