Solving Tx=y: One Solution & R(T) Condition

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Help for prove this please

Let T\in{L(V,W)}
The equation Tx=y have one solution iff y\in{R(T)}
 
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A couple of questions: when you say "has one solution" do you mean exactly one solution or at least one solution?

Also, do you know the definition of "R(T)"?

It looks to me like this problem is either impossible or trivial!
 
Read carefully and try to understand without any doubt whatsoever the definition of R(T).
 

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