Just as in case of #f(x)=(x-2)^2+3#, #f# is a function of #x# and when we try to draw such a function on say Cartesian coordinates, we use #y=f(x)#. But #x# and #y# are just two variables and nature of function does not change, when we replace #x# by #y# and #y# by #x#.
However, a Cartesian graph of the function does change. This is as we always consider #x# as horizontal axis and #y# as vertical axis. We do not reverse these axes, but why we do not do that, because everybody understands that way and no body wants any confusion.
Similarly, in #x=(y-2)^2+3# we have #x# as a function of #y# which can be written as #x=f(y)#.
Further #x=(y-2)^2+3# is an equation with two variables and hence we can express it both as #x=f(y)# as well as #y=f(x)#. In fact solving for #y# we get #y=sqrt(x-3)+2#
However, there is a limitation as in #x=f(y)#, we find there is an #x# for all values of #y#, but in #y=f(x)#, #y# is not defined for #x<3#.
