What is the inverse equation of the function, y= 3x-6?

1 Answer

f^-1(x)=1/3x+2

Explanation:

Concept

f^(-1)(x) (inverse of f(x)) means to switch the x and y variables in the equation f(x)
This means f^(-1)(x)=f(y)

Solving

  • Given function f(x)=3x-6, then f^(-1)(x)\rArr\color(indianred)(x=3y-6)
  • We must isolate the y in f^(-1)(x) to get the proper form of the inverse.
    x=3y-6
    x+6=3y
    x/\color(red)(3)+6/\color(red)(3)={\cancel(3)y}/\cancel(\color(red)(3))
    y=1/3x+2

f^-1(x) = 1/3x+2