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

$\begin{gathered} y=\frac{3x+4}{5} \\ x=\frac{3y+4}{5} \end{gathered}$

step 2

solve for y in the equation

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

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

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

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