SOLUTION: Find the inverse of the function, f^-1(x), if it exists. f(x)= -2 - 5x / 4 + 5x, assume x can not equal -0.8 How do you do this?

Algebra ->  Inverses -> SOLUTION: Find the inverse of the function, f^-1(x), if it exists. f(x)= -2 - 5x / 4 + 5x, assume x can not equal -0.8 How do you do this?      Log On


   

Question 932707: Find the inverse of the function, f^-1(x), if it exists. f(x)= -2 - 5x / 4 + 5x, assume x can not equal -0.8
How do you do this?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The idea is to replace f(x) with y, swap x and y, and then solve for y like so...


f%28x%29=+%28-2-5x%29%2F%284+%2B+5x%29


y=+%28-2-5x%29%2F%284+%2B+5x%29


x=+%28-2-5y%29%2F%284+%2B+5y%29


x%284+%2B+5y%29=+-2-5y


4x+%2B+5xy=+-2-5y


4x+%2B+5xy%2B5y=+-2


5xy%2B5y=+-2-4x


5xy%2B5y=+-4x-2


y%285x%2B5%29=+-4x-2


y=+%28-4x-2%29%2F%285x%2B5%29


So the inverse is

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