Question: Plotting without displaying particular parts of a function

I have a small problem.
I'd like to plot 2 functions in a graph and be able to hide a function for a particular part of the graph.

The functions are:

f:=t->3*t-t^2 and g:=t->2*t
When i plot these functions, I would like to hide the function f(t) for f(t)<1 and I'd like to hide g(t) for g(t)>1.

How can this be accomplished?

Thanks in advance!

 

 

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