SOLUTION: Find the inverse of the function. {{{f(x) = (-5x+4)/(-8x-7)}}} I know the answer is {{{(7x+4)/(-8x+5)}}} but how do I solve this?

Algebra ->  Functions -> SOLUTION: Find the inverse of the function. {{{f(x) = (-5x+4)/(-8x-7)}}} I know the answer is {{{(7x+4)/(-8x+5)}}} but how do I solve this?      Log On


   



Question 1039794: Find the inverse of the function.
f%28x%29+=+%28-5x%2B4%29%2F%28-8x-7%29
I know the answer is %287x%2B4%29%2F%28-8x%2B5%29 but how do I solve this?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The basic outline of finding the inverse is to

step 1) Replace f(x) with y

step 2) Swap x and y

step 3) solve for y


Let's use this outline to get...


f%28x%29+=+%28-5x%2B4%29%2F%28-8x-7%29

y+=+%28-5x%2B4%29%2F%28-8x-7%29 Replace f(x) with y

x+=+%28-5y%2B4%29%2F%28-8y-7%29 Swap x and y. Now isolate y.

x%28-8y-7%29+=+-5y%2B4

-8xy-7x+=+-5y%2B4

-8xy-7x%2B7x+=+-5y%2B4%2B7x

-8xy+=+-5y%2B4%2B7x

-8xy%2B5y+=+-5y%2B4%2B7x%2B5y

-8xy%2B5y+=+4%2B7x

y%2A%28-8x%2B5%29+=+4%2B7x

y+=+%284%2B7x%29%2F%28-8x%2B5%29

y+=+%287x%2B4%29%2F%28-8x%2B5%29


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Final Answer:

The inverse function is