x is a connected space and y is a discrete space prove that the two maps f,g:x to y are homotopic if and only if f=g

x is a connected space and y is a discrete space prove that the two maps
f,g:x to y are homotopic if and only if f=g

x is a connected space and y is a discrete space prove that the two maps
f,g:x to y are homotopic if and only if f=g I am trying to solve few
problems in algebraic topology,but i don't have deep knowledge in the
subject, i guess the reverse direction of proof is trivial.but i am struck
with the forward direction. does the proof include stuff like "for
continuous image of connected set to be discrete the map should be
constant".i am a bit confused with the problem can someone help me out?