Question

QUESTÃO 1: Sejam as funções f(x) = x² - x -10 e g(x) = 3x – t. Sabendo que f(g(1)) = 2 , calcule t

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\mathsf{f(x) = x^2 - x - 10}$

$\mathsf{g(x) = 3x - t}$

$\mathsf{g(1) = 3.1 - t}$

$\mathsf{g(1) = 3 - t}$

$\mathsf{f(g(1)) = 2}$

$\mathsf{(3 - t)^2 - (3 - t) - 10 = 2}$

$\mathsf{(9 - 6t + t^2) - (3 - t) - 10 = 2}$

$\mathsf{9 - 6t + t^2 - 3 + t - 10 = 2}$

$\mathsf{9 - 6t + t^2 - 3 + t - 10 - 2 = 0}$

$\mathsf{t^2 - 5t - 6 = 0}$

$\mathsf{\Delta = b^2 - 4ac}$

$\mathsf{\Delta = (-5)^2 - 4.1.(-6)}$

$\mathsf{\Delta = 25 + 24}$

$\mathsf{\Delta = 49}$

$\mathsf{t = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{-(-5) \pm \sqrt{49}}{2} = \dfrac{5 \pm 7}{2} \rightarrow \begin{cases}\mathsf{t' = \dfrac{5 + 7}{2} = \dfrac{12}{2}= 6}\\\\\mathsf{t'' = \dfrac{5 - 7}{2} = \dfrac{-2}{2} = -1}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{6;-1\}}}}$