Originally posted by golfer1I case you dont know f(x)= 2 is a horizantal line. the (+2) technically shifts the graph of f(x) =2 to the left 2 units, but on a horizantal line nothing happens, so in general f(x + a ) = 2 for all real numbers a....
f(x)= 2 for all real numbers x. What is f(x+2)?
Originally posted by 3v1l5w1ngenerally when someone says f(x) = ..., for all real numbers x, I assume R to be the domain.
yeah, but consider a slight modification of the Dirichlet's function
f(x) = 2 if x is real, and f(x) = 0 if x is complex ... now you have two answers...
or f(x) = 2 if x is real, and f(x) = Re(x) if x is complex ... now the range of the function is the entire R.
in other words, the question as posed is [b]incomplete, without stating the domain of the original function.[/b]