Question

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

Answer 1

Answer: x^3/3+2x^2

hope this helps!!

Answer 2

`g^(-1)(x)=-1\pm(√(x(x+3)))/(x)`

Explanation:

Given :
`g(x)= (3)/(x^2+2x)`

To find :
`g^(-1)(x)`

Solution :

We have given the function,

`g(x)= (3)/(x^2+2x)`

To find inverse let y=g(x)

`y= (3)/(x^2+2x)`

Replace the value of x and y,

`x=(3)/(y^2+2y)`

Solve for y,

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

`xy^2+2xy-3=0`

Solve by quadratic formula,

i.e. The equation
`ax^2+bx+c=0` has solution

`x=(-b\pm√(b^2-4ac))/(2a)`

On comparing, a=x , b=2x , c=-3

`y=(-(2x)\pm√((2x)^2-4(x)(-3)))/(2(x))`

`y=(-2x\pm√(4x^2+12x))/(2x)`

`y=(-2x\pm2√(x(x+3)))/(2x)`

`y=-1\pm(√(x(x+3)))/(x)`

Therefore, The inverse of g(x) is

`g^(-1)(x)=-1\pm(√(x(x+3)))/(x)`