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

1 Answer
seol · EZ as pi · Daniel L.
Nov 20, 2016

f^-1(x)=1/3x+2f−1(x)=13x+2

Explanation:

Concept

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

Solving

  • Given function f(x)=3x-6f(x)=3x−6, then f^(-1)(x)\rArr\color(indianred)(x=3y-6)f−1(x)⇒x=3y−6
  • We must isolate the yy in f^(-1)(x)f−1(x) to get the proper form of the inverse.
    x=3y-6x=3y−6
    x+6=3yx+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

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