Question

For the function f (x)= x / 2 x + 3 find f - 1(x)

Answer 1

1) In order to find the inverse function of that function, let's do it step by step

Given the function, remember f(x) and y is the same thing.

`f(x)=(x)/(2x+3)`

Swap the x for y:

`\begin{gathered} y=(x)/(2x+3) \\ x=(y)/(2y+3) \\ \text{Cross multiply:} \\ x(2y+3)\text{ =y} \\ 2xy\text{ +3x = y} \\ \text{Subtract y from both sides} \\ 2xy-y+3x=0 \\ Subtract\text{ 3x from both sides} \\ 2xy-y=-3x \\ \text{Write the left side as a factor} \\ y(2x-1)\text{ =-3x} \\ \text{Divide both sides by (2x-1)} \\ y=(-3x)/(2x-1) \\ \text{Write the proper notation:} \\ f^(-1)(x)=(-3x)/(2x-1) \end{gathered}`

2) Then the inverse function for that one is:

`f^(-1)(x)=(-3x)/(2x-1)`