Answer:
3
Step-by-step explanation:
This is a piece-wise function. The domain [x-values] is broken down into parts.
To evaluate this type of functions, we see in WHICH PART of the DOMAIN does the questions ask to look for.
The question asks for [tex]g(3)[/tex] , the value of the function at [tex]x=3[/tex]
In which of the 3 parts does [tex]x=3[/tex] fall into?
The domain condition, [tex]x\geq3[/tex] , in the last part tells us that it is GREATER THAN OR EQUAL TO 3. So [tex]x=3[/tex] falls in this part of the function, which is [tex]6-x[/tex]
We can simply substitute 3 in [tex]x[/tex] of that part and get our desired answer. So,
[tex]6-x\\6-(3)\\3[/tex]
The value of [tex]g(3)=3[/tex]
