Question

esboce o gráfico de f (x) = 2 - cos x indicando imagem

Answer 1

✅ Seja a função trigonométrica circular:

     $\Large\displaystyle\begin{gathered} f(x) = 2 - \cos(x)\end{gathered}$

Para montarmos o gráfico podemos encontrar 5 pontos. Então, calculando cada um dos 5 pontos, temos:

• Quando x = 0:

           $\Large\displaystyle\begin{gathered} f(0) = 2 - \cos(0) = 2 - 1 = 1\end{gathered}$

           $\Large\displaystyle\begin{gathered} \therefore\:\:\:A(0, 1)\end{gathered}$

• Quando x = π/2:

           $\Large\displaystyle\begin{gathered} f\bigg(\frac{\pi}{2}\bigg) = 2 - \cos\bigg(\frac{\pi}{2}\bigg) = 2 - 0 = 2\end{gathered}$

           $\Large\displaystyle\begin{gathered} \therefore\:\:\:B\bigg(\frac{\pi}{2}, 2\bigg)\end{gathered}$

• Quando x = π:

           $\Large\displaystyle\begin{gathered} f(\pi) = 2 - \cos(\pi) = 2 - (-1) = 3\end{gathered}$

            $\Large\displaystyle\begin{gathered} \therefore\:\:\:C(\pi, 3)\end{gathered}$

• Quando x = (3π)/2:

           $\Large\displaystyle\begin{gathered} f\bigg(\frac{3\pi}{2}\bigg) = 2 - \cos\bigg(\frac{3\pi}{2}\bigg) = 2 - 0 = 2\end{gathered}$

            $\Large\displaystyle\begin{gathered} \therefore\:\:\:D\bigg(\frac{3\pi}{2}, 2\bigg)\end{gathered}$

• Quando x = 2π

            $\Large\displaystyle\begin{gathered} f(2\pi) = 2 - \cos(2\pi) = 2 - 1 = 1\end{gathered}$

             $\Large\displaystyle\begin{gathered} \therefore\:\:\:E(2\pi, 1)\end{gathered}$

Além disso temos:

       $\Large\displaystyle\begin{gathered} \textrm{Dominio} = \mathbb{R}\end{gathered}$

       $\Large\displaystyle\begin{gathered} \textrm{Contra Dominio} = \mathbb{R}\end{gathered}$

       $\Large\displaystyle\text{ \begin{gathered} \textrm{Imagem} = \{y\in\mathbb{R}\,|\,1\leq y \leq3\} = \left[1,\,3\right]\end{gathered} }$

Saiba mais:

1. https://brainly.com.br/tarefa/47823956
2. https://brainly.com.br/tarefa/52082085

Veja também a solução gráfica da questão represntada na figura: