Question

considere a função f R→R definida por f(x) = x² + 2x -3. Calcule f(-3), f(-2), f(-1), f(0), f(1), f(2)

Answer 1

Para calcular qualquer função que seja, basta alterarmos o valor dado pela incógnita x na função geral.

$\large\begin{array}{lr} \sf f(x) = x^{2} + 2x -3\end{array} \left\{\begin{array}{ll}\sf x= -3\\\sf x= -2\\\sf x= -1\\\sf x= 0\\\sf x= 1\\\sf x=2\end{array}\right.$

Vamos primeiramente trocar a função inteira por x = -3. vamos lá.

$\large\begin{array}{lr} \sf f(x) = x^{2} + 2x -3\\\\\sf f(-3) = (-3)^{2} + 2(-3) -3 \\\\\sf f(-3) = 9 + (-6)-3\\\\\sf f(-3) = 9 -6-3\\\\\sf f(-3) = 9-9\\\\\sf f(-3) = \underline{\boxed{\blue{\sf 0}}}\end{array}$

Agora iremos trocar a função inteira por x = -2. ficando assim:

$\large\begin{array}{lr} \sf f(x) = x^{2} + 2x -3\\\\\sf f(-2) = (-2)^{2} + 2(-2) -3 \\\\\sf f(-2) = 4 + (-4)-3\\\\\sf f(-2) = 4 -4-3\\\\\sf f(-2) = 4-7\\\\\sf f(-2) = \underline{\boxed{\blue{\sf -3}}}\end{array}$

Agora iremos trocar a função inteira por x = -1. ficando assim:

$\large\begin{array}{lr} \sf f(x) = x^{2} + 2x -3\\\\\sf f(-1) = (-1)^{2} + 2(-1) -3 \\\\\sf f(-1) = 1 + (-2)-3\\\\\sf f(-1) = 1 -2-3\\\\\sf f(-1) = 1-5\\\\\sf f(-1) = \underline{\boxed{\blue{\sf -4}}}\end{array}$

Agora iremos trocar a função inteira por x = 0. ficando assim:

$\large\begin{array}{lr} \sf f(x) = x^{2} + 2x -3\\\\\sf f(0) = (0)^{2} + 2(0) -3 \\\\\sf f(0) = 0 + 0-3\\\\\sf f(0) = \underline{\boxed{\blue{\sf -3}}}\end{array}$

Agora iremos trocar a função inteira por x = 1. ficando assim:

$\large\begin{array}{lr} \sf f(x) = x^{2} + 2x -3\\\\\sf f(1) = (1)^{2} + 2(1) -3 \\\\\sf f(1) = 1 + 2-3\\\\\sf f(1) = 3-3\\\\\sf f(1) = \underline{\boxed{\blue{\sf 0}}}\end{array}$

Por fim basta fazermos a mesma coisa só que iremos trocar agora a função inteira por x = 2, ficando assim:

$\large\begin{array}{lr} \sf f(x) = x^{2} + 2x -3\\\\\sf f(2) = (2)^{2} + 2(2) -3 \\\\\sf f(2) = 4 + 4-3\\\\\sf f(2) = 8-3\\\\\sf f(2) = \underline{\boxed{\blue{\sf 5}}}\end{array}$

Concluirmos então que:

$\begin{array}{lr} \sf f(-3) \rightarrow \underline{\boxed{\red{\sf 0}}}\\\\ \sf f(-2)\rightarrow \underline{\boxed{\red{\sf -3}}}\\\\\sf f(-1) \rightarrow \underline{\boxed{\red{\sf -4}}}\\\\\sf f(0)\rightarrow \underline{\boxed{\red{\sf -3}}}\\\\\sf f(1) \rightarrow \underline{\boxed{\red{\sf 0}}}\\\\\sf f(2) \rightarrow \underline{\boxed{\red{\sf 5}}}\end{array}$

Espero ter ajudado.

Bons estudos.

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