### Home > PC3 > Chapter 1 > Lesson 1.2.2 > Problem1-84

1-84.

Write the equation of the inverse for each of the following functions and state any domain restrictions needed so that the original function and its inverse are inverses of each other.

1. $f(x)=\frac{3x}{x+2}$

$y=\frac{3x}{x+2}$

$y(x+2)=3x$

$yx+2y=3x$

$yx-3x=-2y$

$x(y-3)=-2y$

$x=\frac{-2y}{y-3}$

$f^{-1}(x)=\frac{-2x}{x-3}$

1. $h(x)=\sqrt{3x-12}$

Follow the steps in part (a).

What are the domain and range of the original function?
How does this affect the domain of the inverse function?