How do u write function notation and what variable does function notation replace

If f(x) = 2x+1; Prove f(3+1) =f(3)+f(1)
Proof: 2(3+1)+1 = 2(3)+1 + 2(1)
6+2+1 = 6+1+2
9 = 9
Therefore: f(3+1) =f(3)+f(1)

this is NOT the answer just a question i got on my test its a example

The the ratio