Math question 10 points first one ez easy inverse?

Question

find the inverse of
g(x)=3/(x^2+2x)

how do you do it?

Answer 1

To get the inverse function, just reverse x and y and solve for y.
g(x) = 3 / (x² + 2x)

Reverse x and y:
x = 3 / (y² + 2y)

Multiply by y² + 2y on both sides and divide by x, to get y terms out of the denominator and by themselves:
y² + 2y = 3/x

Now you want to complete the square. To complete the square, take the coefficient on the y term (2), take half (1) and square it (1). Add this to both sides of the equation:
y² + 2y + 1 = 3/x + 1

Because we have "completed the square" we can rewrite the left expression as a perfect square:
(y + 1)² = 3/x + 1

Take the square root of both sides (be sure to account for +/- roots):
y + 1 = ±sqrt(3/x + 1)

Subtract 1 from both sides:
y = -1 ± sqrt(3/x + 1)

So your inverse function is:
g'(x) = -1 ± sqrt(3/x + 1)

Note: as a check, I graphed both functions. Notice how g'(x) is a perfect reflection across the line y = x.

Answer 2

reverse x and y
x=3/(y^2+2y)
y^2+2y=3/x
completing the square on left side
(y^2+2y+1)-1=3/x
(y+1)^2=3/x +1
y+1=+-sqrt(3x+1)
y=+-sqrt(3x+1) -1

Answer 3

g^(-1)(x) = -1 + sqrt(1+3/x) for x >0

Answer 4

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