Question

Seja a função f: R --> R por f(x+1) = f(x) + x. Sabendo que f(1) = 2, determine o valor de f(3) + f(4) - f(2).

Answer 1

$f(x+1) = f(x) + x\\\\ f(1+1)=f(1)+1\rightarrow f(2)=2+1\rightarrow \boxed{f(2)=3}\\\\ f(2+1)=f(2)+2\rightarrow f(3)=3+2\rightarrow \boxed{f(3)=5}\\\\ f(3+1)=f(3)+3\rightarrow f(4)=5+3\rightarrow \boxed{f(4)=8}\\\\ \Rightarrow f(3)+f(4)-f(2)=5+8-3= \boxed{10}$