SOLUTION: Find the inverse of the one-to-one function. f(x) = 6/x-7 f^-1(x)=______ (the f^-1 is separate from the (x), not ^-1(x) )

Algebra ->  Rational-functions -> SOLUTION: Find the inverse of the one-to-one function. f(x) = 6/x-7 f^-1(x)=______ (the f^-1 is separate from the (x), not ^-1(x) )      Log On


   



Question 390987: Find the inverse of the one-to-one function.
f(x) = 6/x-7
f^-1(x)=______
(the f^-1 is separate from the (x), not ^-1(x) )

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%286%2Fx%29-7
1. Replace f%28x%29 with y.
y=+6%2Fx-7
2. Reverse the roles of x and y, that is replace every occurrence of x with y and every occurrence of y with x.
x=+6%2Fy-7
3. Solve for y in terms of x.
x=+6%2Fy-7
x+%2B+7=+6%2Fy.........multiply by y
y%28x+%2B+7%29=+6
y=+6%2F%28x+%2B+7%29

4. Replace y with f%5E-1%28x%29.
f%5E-1%28x%29=+6%2F%28x+%2B+7%29