Question

What is the inverse of
`f(x) = √(3x - 2)` for
`x \geq (2)/(3)`

Answer 1

• 
  `f^(-1)(x)=\cfrac{x^2+2}{3}`

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Given function

• 
  `f(x)=√(3x-2)`

Find its inverse, substitute x with y and f(x) with x

• 
  `x=√(3y-2)`
• 
  `x^2=3y-2`
• 
  `3y=x^2+2`
• 
  `y=\cfrac{x^2+2}{3}`

The inverse of f(x) is

• 
  `f^(-1)(x)=\cfrac{x^2+2}{3}`