What are the major trends and specialties in psychology?

Mental activities such as thinking, memory, learning, reasoning, perception and language are all part of this psychology specialty. Cognitive psychology is a very influential psychology specialty as it affects many other psychology specialties, such as education psychology, social psychology and development psychology.

to answer your question:

f(x)= a^x.  if x=0, f(x)=1  if x=1, f(x)=a  if x=1, f(x)=a^a