Kenneth Rosen Edition 7 Exercise 2.3 Question 29 (Page No. 154)

Question

Show that the function $f(x)=|x|$ from the set of real numbers to the set of nonnegative real numbers is not invertible, but if the domain is restricted to the set of nonnegative real numbers, the resulting function is invertible.

Answer 1

given function f(x) = |x|

the function is not one to one { f(2) = 2 = f(-2) }. so it is not invertible.

if domains changes to non negative real numbers then f(x) = x

which is one to one and it is invertible.