Question

Dadas as funções F(x) = 3x +2 e g(x) = − x² + 5, determine F[g(-1)]:
a (4)
b (4)
c (10)
g (6)
e (12)​

Answer 1

✅ Após resolver os cálculos, concluímos que o valor numérico da seguinte composição de funções "f(g(-1))" é:

            $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf f(g(-1)) = 14\:\:\:}}\end{gathered} }$

Sejam os dados:

                $\Large\begin{cases} f(x) = 3x + 2\\g(x) = -x^{2} + 5\\f(g(-1)) = \:?\end{cases}$

Para resolver esta questão devemos:

• Calcular a seguinte função composta "f(g(x))".

           $\Large\displaystyle\begin{gathered} f(g(x)) = 3\cdot\left[g(x)\right] + 2\end{gathered}$

                             $\Large\displaystyle\begin{gathered} = 3\cdot\left[-x^{2} + 5\right] + 2\end{gathered}$

                             $\Large\displaystyle\begin{gathered} = -3x^{2} + 15 + 2\end{gathered}$

                              $\Large\displaystyle\begin{gathered} = -3x^{2} + 17\end{gathered}$

       Portanto "f(g(x))" é:

                    $\Large\displaystyle\begin{gathered} f(g(x)) = -3x^{2} + 17\end{gathered}$

• Obter o valor numérico de "f(g(-1))".

               $\Large\displaystyle\begin{gathered} f(g(-1)) = -3\cdot(-1)^{2} + 17\end{gathered}$

                                    $\Large\displaystyle\begin{gathered} = -3\cdot1 + 17\end{gathered}$

                                    $\Large\displaystyle\begin{gathered} = -3 + 17\end{gathered}$

                                    $\Large\displaystyle\begin{gathered} = 14\end{gathered}$

✅ Portanto, o valor numérico de "f(g(-1))" é:

                $\Large\displaystyle\begin{gathered} f(g(-1)) = 14\end{gathered}$

$\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered} }$

Saiba mais:

1. https://brainly.com.br/tarefa/51909132
2. https://brainly.com.br/tarefa/51912907
3. https://brainly.com.br/tarefa/52553254
4. https://brainly.com.br/tarefa/52595907
5. https://brainly.com.br/tarefa/52659899
6. https://brainly.com.br/tarefa/52828354
7. https://brainly.com.br/tarefa/52835460
8. https://brainly.com.br/tarefa/52847909
9. https://brainly.com.br/tarefa/52955065
10. https://brainly.com.br/tarefa/53206705
11. https://brainly.com.br/tarefa/53282916
12. https://brainly.com.br/tarefa/15134362
13. https://brainly.com.br/tarefa/53743816

$\Large\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Observe \:o\:Gr\acute{a}fico!!\:\:\:}}}\end{gathered} }$