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

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Answer 1 · 2016-11-20T06:26:00

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

Concept

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

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.
$x=3y-6$
$x+6=3y$
$x/\color(red)(3)+6/\color(red)(3)={\cancel(3)y}/\cancel(\color(red)(3))$
$y=1/3x+2$

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