Question

Na função f(x) = 3x – 2 / 3 – x. Calcule f(-3/4) + f(4/3)

Answer 1

Resposta:

$\frac{1}{15}$

Explicação passo-a-passo:

$f(-\frac{3}{4}) = \dfrac{3(-\frac{3}{4}) - 2}{3-(-\frac{3}{4})} = \dfrac{-\frac{3\times3}{4} - 2}{3+\frac{3}{4}} = \dfrac{-\frac{9}{4} - 2\times \frac{4}{4}}{3\times \frac{4}{4}+\frac{3}{4}}=\\\\=\dfrac{-\frac{9}{4} - \frac{2\times 4}{4}}{ \frac{3\times4}{4}+\frac{3}{4}} = \dfrac{\frac{-9 - 2\times 4}{4}}{ \frac{3\times4+3}{4}} = \dfrac{\frac{-9 - 8}{4}}{ \frac{12+3}{4}} = \dfrac{\frac{-17}{4}}{ \frac{15}{4}} = -\frac{17}{4} \times (\frac{15}{4})^{-1} = -\frac{17}{4} \times \frac{4}{15} =$

$= - \frac{17\times 4}{4 \ times 15} = - \frac{17}{15}$

$f(\frac{4}{3}) = \dfrac{3(\frac{4}{3}) - 2}{3-(\frac{4}{3})} = \dfrac{\frac{3\times4}{3} - 2}{3-\frac{4}{3}} = \dfrac{4 - 2}{3\times \frac{3}{3}-\frac{4}{3}}=\dfrac{2}{ \frac{3\times3}{3}-\frac{4}{3}} = \\\\=\dfrac{2}{ \frac{9-4}{3} } = 2 \times (\frac{5}{3})^{-1} = 2 \times \frac{3}{5} = \frac{6}{5}$

$f(-\frac{3}{4} ) + f(\frac{4}{3} ) = -\frac{17}{15} + \frac{6}{5} = -\frac{17}{15} + \frac{6\times 3}{5\times 3} = \frac{-17+6\times 3}{15} = \frac{1}{15}$