Answer :
See
Domain is (-3,oo)
Put -3 on f(x)
- f(-3)=2(-3)+3=-6+3=-3
Range is
- (-3,oo)
Its unclear
Find x values then
- 2x+3=-1=>x=-2
- 2x+3=0=>x=-1.5
- 2x+3=3=>x=0
- 2x+3=6=>x=1.5
Every no is present in range
If domain of your question is something different from (-3,oo) ,then only the answer is possible,Let me know about it .I will change accordingly