Convert the angle 0 = 3pie/5 radians to degrees

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Ответ:

xchloee

16.12.2022

Mathematics

$g^{-1}(x) = -1 \pm\sqrt{\dfrac{3}{x} + 1}$

Step-by-step explanation:

$g(x) = \dfrac{3}{x^2 + 2x}$

1. Replace g(x) with y.

$y = \dfrac{3}{x^2 + 2x}$

2. Switch x and y.

$x = \dfrac{3}{y^2 + 2y}$

3. Solve for y.

x(y^2 + 2y) = 3

$y^2 + 2y = \dfrac{3}{x}$

Complete the square in y:

$y^2 + 2y + 1 = \dfrac{3}{x} + 1$

$(y + 1)^2 = \dfrac{3}{x} + 1$

$y + 1 = \pm\sqrt{\dfrac{3}{x} + 1}$

$y = -1 \pm\sqrt{\dfrac{3}{x} + 1}$

4. Replace y with g^-1(x) .

$g^{-1}(x) = -1 \pm \sqrt{\dfrac{3}{x} + 1}$

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