(a) Let f : R -> R be defined by f(x) = x^2. Show that f(x) has no inverse function.

(b) Let g : (0,inf) -> R be defined by g(x) = x^2. Show that g(x) has an inverse function.

Guest Jun 18, 2021

#1**+2 **

A function does not have an inverse function when 2 different x values can produce the same y value.

f(-3) = 9

f(3) = 9

So if we were to inverse it, f(9) could be 3 or -3, making it not a function.

Think about why g(x) has an inverese.

Can 2 different x in the domain produce the same y?

=^._.^=

catmg Jun 18, 2021