Unless you have some restriction on the possible values of x (on the domain) this function does not have an inverse!
RRH gets to
and then says that
but there are
two values of y whose square is x+ 4.
If the original function is "
with domain
", THEN
with domain
.
If the original function is "
with domain
, THEN
with domain
RRH is also wrong when he writes
. For example, if x= 1,
which is certainly not equal to
.
Follow the pattern RRH used (which is correct). From
(which has natural domain all real numbers except 2), the inverse function is given by
, where I have swapped x and y. Now solve for y.