Question

Find the inverse of f(x) = (3x+4)/5

Answer 1

hello

to find the inverse of a funtion, we'll follow some basic steps to get there

step 1

replace x with y or the notation you want to represent the inverse with

f(x) = (3x+4)/5

replace x with y and y with x

`\begin{gathered} y=(3x+4)/(5) \\ x=(3y+4)/(5) \end{gathered}`

step 2

solve for y in the equation

`\begin{gathered} x=(3y+4)/(5) \\ \text{make y the subject of formula} \\ \text{cross multiply both sides } \\ 5x=3y+4 \\ 3y=5x-4 \\ y=(5x-4)/(3) \end{gathered}`

now replace f(x) with f(x)^-1

f(x)^-1 = (5x - 4) / 3

`\text{note: f(x)\textasciicircum -1 represent f(x)}^(-1)\text{ which is the inverse of the function}`