Question

Seja função : ℝ → ℝ, definidas por f(x) = x^2 - 6/2 para todo x ∈ ℝ. Determine "a", de tal forma que f(a) = f(a-4).

Answer 1

$f(a)~=~f(a-4)\\\\\\(a)^2-\frac{6}{2}~=~(a-4)^2-\frac{6}{2}\\\\\\a^2-3~=~a^2-8a+16-3\\\\\\a^2-a^2+8a~=~16-3+3\\\\\\8a~=~16\\\\\\a~=~\frac{16}{8}\\\\\\\boxed{a~=~2}$