Question

f(x) =x − 4 funcion inversa
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x + 4

Answer 1

Respuesta:

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

Explicación paso a paso:

y = f(x)

$y = \frac{x - 4}{x + 4}$

y(x + 4) = x - 4

xy + 4y = x - 4

xy - x = -4 - 4y

x(y - 1) = -4 - 4y

$x = \frac{-4 - 4y}{y - 1}$

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

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