Question

$f ( x ) = \frac { 2 x + 5 } { 3 }$
Obtenha f-¹(x)

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Answer 1

Resposta:

$\sf f(x)=y=\dfrac{2x+5}{3}$

Pra obter a inversa de f(x), comute x e y e por fim isole y:

$\sf y=\dfrac{2x+5}{3}$

$\sf x=\dfrac{2y+5}{3}$

$\sf3x=2y+5$

$\sf2y=3x-5$

$\sf y=\dfrac{3x-5}{2}$

$\red{\boxed{\sf f(x)^{-1}=\dfrac{3x-5}{2}}}~\rightarrow~\sf notac_{_{\!\!s}}\tilde{a}o~usual.$