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