# HELP! Inverse Fuction

• Sep 9th 2008, 03:03 PM
asweet1
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.
• Sep 9th 2008, 03:10 PM
skeeter
Quote:

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 $\displaystyle y = g(x)$

$\displaystyle y = 900 + 100x$

step 1 ... swap x and y

$\displaystyle x = 900 + 100y$

step 2 ... solve for y

$\displaystyle x - 900 = 100y$

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

so ...

$\displaystyle g^{-1}(x) = \frac{x-900}{100}$
• Sep 9th 2008, 03:12 PM
11rdc11
$\displaystyle c = 900 + 100x$

To get the inverse solve for x

$\displaystyle c - 900 = 100x$

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

Now just swap variables

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

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