# Math Help - HELP! Inverse Fuction

1. ## HELP! Inverse Fuction

The cost of producing x air conditioners is c=g(x)=900+100x. Find a formula for the inverse function g^-1(c). I don't understand inverse functions at all. Please help me.

2. Originally Posted by asweet1
The cost of producing x air conditioners is c=g(x)=900+100x. Find a formula for the inverse function g^-1(c). I don't understand inverse functions at all. Please help me.
let $y = g(x)$

$y = 900 + 100x$

step 1 ... swap x and y

$x = 900 + 100y$

step 2 ... solve for y

$x - 900 = 100y$

$\frac{x-900}{100} = y$

so ...

$g^{-1}(x) = \frac{x-900}{100}$

3. $c = 900 + 100x$

To get the inverse solve for x

$c - 900 = 100x$

$\frac{c}{100} -9 = x$

Now just swap variables

$c = \frac{x}{100} -9$

There is your inverse

$g^{-1}(x) = \frac{x}{100} -9$