Given g(x) =
rac{3}{x^2+2x}" align="absmiddle" class="latex-formula"> find g^-1(x)
2 answers:
We know that g(x) = \frac{3}{x^2+2x}
We have to find g^-1(x) or inverse of g(x)
Inverse of g(x) can be determined by equating g(x) to y, and determining the value of x in terms of y
g(x) = y = \frac{3}{x^2+2x}
⇒ y × (x² + 2x) = 3
⇒ yx² + 2xy = 3
⇒ yx² + 2yx - 3 = 0
Determining the roots of x using:
x =
OR x =
, where a is coefficient of x², b is coefficient of x, and c is the constant
⇒ x =
OR x = 
⇒ x =
OR x = 
Hence, g^-1(x) =
OR x = 
<h2>
Answer:</h2>
We get:

<h2>
Step-by-step explanation:</h2>
In order to find the inverse of a given function f(x) we follows following steps:
1) Substitute f(x)=y
2) Interchange x and y
3) Solve for y.
Here we have the function g(x) as follows:

Now, we substitute:

i.e.

Now, we interchange x and y:

We know that the solution to the quadratic equation of the type:

is given by:

Here,

Hence, the solution is:

i.e.

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