Seven cookies of radius $1$ inch are cut from a circle of cookie dough, as shown. Neighboring cookies are tangent, and all excep
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Because they're not inverses, not exactly. is not invertible on its entire domain because it's not one-to-one. There are infinitely many values of
such that
, for example.
The standard function has a domain of
and outputs values between
and
. This means that its inverse,
, is indeed its inverse as long as
.
is larger than
and thus does not fall in the "invertible part" of the domain of
. We have
which is a value between -1 and 1, so that
If we wanted to recover , we'd have to redefine
or define a new inverse function that works on a different branch of the domain of
.