Question

1x + 1Given: f(x)=52 + 3Find the inverse function, f-1(x).

Answer 1

`f^(-1)(x)\text{ = }(1-3x)/(5x-1)`

Step-by-step explanation:

Here, we want to get the inverse of the given function

We start by equating the expression to y and making x the formula subject as follows:

`\begin{gathered} y\text{ = }(x+1)/(5x+3) \\ \\ y(5x+3)=x+1_{} \\ 5xy\text{ + 3y = x + 1} \\ 5xy-x\text{ = 1-3y} \\ x(5y-1)\text{ = 1-3y} \\ x\text{ = }(1-3y)/(5y-1) \end{gathered}`

Substitute x for y:

`f^(-1)(x)\text{ = }(1-3x)/(5x-1)`