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

Find f(x) where f(x) = 3x+2/x-example-1
User Ecrb
by
6.6k points

1 Answer

9 votes

Answer:


\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:


step - 1 : define


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)

User Alain Gauthier
by
7.4k points