Question

Find the inverse of the function f(x) = log4(3x)+2 (the 4 is down)

Answer 1

we have the function

`f(x)=\log _43x+2`

step 1

Let

y=f(x)

`y=\log _43x+2`

step 2

Exchange the variables (x for y and y for x)

`x=\log _43y+2`

step 3

Isolate the variable y

`\begin{gathered} x=\log _43y+2 \\ (x-2)=\log _43y \\ 4^((x-2))=3y^{} \\ y=(4^((x-2)))/(3) \end{gathered}`

therefore

The inverse function is equal to

`f^(-1)(x)=(4^((x-2)))/(3)`