Question

Find f(x) where
f(x) = 3x+2/x

Answer 1

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

Explanation:

to understand this

you need to know about:

• inverse function
• PEMDAS

given:

• 
  `f(x) = (3x + 2)/(x)`

to find:

• 
  `{f}^( - 1) (x)`

tips and formulas:

inverses of common function

1. 
   `+ < = > -`
2. 
   `* < = > /`
3. 
   `(1)/(x) < = > (1)/(y)`
4. 
   `x ^(n) < = > \sqrt[n]{y}`

let's solve:

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

`step - 2 : solve`

1. 
   `substitute \: y \: for \: f(x) \\ y = (3x + 2)/(x)`
2. 
   `interchange \: x \: and \: y \: and \: swap \: the \: sides \: of \: the \: equation\\ (3y + 2)/(y) = x`
3. 
   `multiply \: both \: sides \: of \: the \: equation \: by \: y \\ (3y + 2)/(y) * y = x * y \\ 3y + 2 = xy`
4. 
   `move \: the \: constant \: and \: the \: expression \: to \: the \: right \: and \: left \: hand \: sides \: and \: change \: its \: sign \: respectively \\ 3y - xy = - 2`
5. 
   `factor \: out \: y \: from \: the \: expression \\ (3 - x)y = - 2`
6. 
   `divide \: both \: sides \: by \: 3 - x \\ ((3 - x)y)/((3 - x)) = ( - 2)/(3 - x)`
7. 
   `y = ( - 2)/(3 - x)`

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