Question

Encontre a Função Inversa f(x)=(4x-1)/(2x+3)?
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Answer 1

Oie, Td Bom?!

$f(x) = \frac{4x - 1}{2x + 3}$

• Substitua $f(x)⟶y$

$y = \frac{4x - 1}{2x + 3}$

• Intersete $x⟷y$

$x = \frac{4y - 1}{2y + 3}$

$\frac{4y - 1}{2y + 3} = x$

$(2y + 3) \: . \: \frac{4y - 1}{2y + 3} = (2y + 3)x$

$4y - 1 = (2y + 3)x$

$4y - 1 = 2xy + 3x$

$4y - 2xy = 3x + 1$

$(4 - 2x)y = 3x + 1$

$(4 - 2)y \div (4 - 2x) = (3x + 1) \div (4 - 2x)$

$y = (3x + 1) \div (4 - 2x)$

$y = \frac{3x + 1}{4 - 2x}$

• Substitua $y⟶f {}^{ - 1} (x)$

$f {}^{ - 1} (x) = \frac{3x + 1}{4 - 2x}$

Att. Makaveli1996