Question

Sendo f(x) = x²-2, determine o valor de x para que f(x) = f(x+1)

Answer 1

Resposta:

$\boxed{\mathtt{\frac{- 1}{2}}}$

Explicação passo-a-passo:

Inicialmente, devemos determinar $\displaystyle \mathtt{f(x + 1)}$. Segue,

$\\ \displaystyle \mathsf{f(x) = x^2 - 2} \\\\ \mathsf{f(x + 1) = (x + 1)^2 - 2} \\\\ \mathsf{f(x + 1) = x^2 + 2x + 1 - 2} \\\\ \boxed{\mathsf{f(x + 1) = x^2 + 2x - 1}}$

Por conseguinte, igualamos... Veja:

$\\ \displaystyle \mathsf{f(x) = f(x + 1)} \\\\ \mathsf{x^2 - 2 = x^2 + 2x - 1} \\\\ \mathsf{x^2 - 2 - x^2 - 2x + 1 = 0} \\\\ \mathsf{- 2 - 2x + 1 = 0} \\\\ \mathsf{- 2x - 1 = 0} \\\\ \boxed{\boxed{\mathsf{x = - \frac{1}{2}}}}$