Question

Seja f:R➡️R uma função, tal que f(x+1) - f(x) = 2x CALCULE:

a) f(20) - f(19)
b) f(71) - f(20)
c) f(12) - f(10)

Answer 1

$f(x+1)-f(x)=2x$

a) $x=19$

$f(20)-f(19)=2\times19$

$\boxed{f(20)-f(19)=38}$

b) $x=70$

$f(71)-f(70)=2\times70$

$\boxed{f(71)-f(70)=140}$

c) Fazendo $x=10$:

$f(11)-f(10)=2\times10$

$f(11)-f(10)=20 \ (i)$

Fazendo $x=11$:

$f(12)-f(11)=2\times11$

$f(12)-f(11)=22 \ (ii)$

Somando $(i)$ e $(ii)$:

$f(11)-f(10)+f(12)-f(11)=20+22$

$\boxed{f(12)-f(10)=42}$