Question

Given g(x)=3/x^2+2x find g^-1(x)

Answer 1

Answer:

Inverse function is: $g^{-1}x=\frac{-x\pm\sqrt{x(x+3)}}{x}$

Step-by-step explanation:

Given Given the function $g(x)=\frac{3}{x^2+2x}$

we have to find the inverse function of g

To find inverse following steps are:

Step 1: Replace g(x) with y

Step 2: Replace every x with a y and every y with x  

Step 3: Solve the equation obtained from Step 2 for y.

Step 4: Replace y with g−1(x).

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

To find the inverse, let $y=\frac{3}{x^2+2x}$

Now, solve for x

$y(x^2+2x)=3$

$yx^2+2yx-3=0$

$x=\frac{-2y\pm\sqrt{4y^2-4y(-3)}}{2y}$

$x=\frac{-2y\pm\sqrt{4y^2+12y}}{2y}$

$x=\frac{-2y\pm2\sqrt{y^2+3y}}{2y}$

$x=\frac{-y\pm\sqrt{y(y+3)}}{y}$

Replace every x with a y and every y with x  , we get

$y=\frac{-x\pm\sqrt{x(x+3)}}{x}$

Replace y with g−1(x).

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

So inverse function is: $g^{-1}x=\frac{-x\pm\sqrt{x(x+3)}}{x}$