Question

Considerando f(x + 1) = f(x) + 2.f(1), e sabendo que f(2) = 4, pode-se afirmar que f(4) vale:

Answer 1

$\mathrm{f(x+1)=f(x)+2.f(1)\ \ \| \ \ f(2)=4\ \ \| \ \ f(4)=\ ?}\\\\ \mathrm{Para\ x=1:}\\\\ \mathrm{f(1+1)=f(1)+2.f(1)\ \to\ f(2)=3.f(1)}\\\\ \mathrm{4=3.f(1)\ \to\ f(1)=\dfrac{4}{3}}\\\\ \mathrm{Para\ x=2:}\\\\ \mathrm{f(2+1)=f(2)+2.f(1)\ \to\ f(3)=4+2.\dfrac{4}{3}}\\\\ \mathrm{f(3)=4+\dfrac{8}{3}\ \to\ f(3)=\dfrac{12+8}{3}\ \to\ f(3)=\dfrac{20}{3}}$

$\mathrm{Para\ x=3:}\\\\ \mathrm{f(3+1)=f(3)+2.f(1)\ \to\ f(4)=\dfrac{20}{3}+2.\dfrac{4}{3}}\\\\ \mathrm{f(4)=\dfrac{20}{3}+\dfrac{8}{3}\ \to\ \mathbf{f(4)=\dfrac{28}{3}}}$