SOLUTION: Given: f(x) = (6x-6)/(3x+3) Find the inverse function, f^-1(x)

Algebra ->  Functions -> SOLUTION: Given: f(x) = (6x-6)/(3x+3) Find the inverse function, f^-1(x)      Log On


   

Question 976196: Given: f(x) = (6x-6)/(3x+3)
Find the inverse function, f^-1(x)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Given: f%28x%29+=+%286x-6%29%2F%283x%2B3%29+
Find the inverse function, f%5E-1%28x%29
since f%28x%29+=+y+, we have
y=+%286x-6%29%2F%283x%2B3%29+......swap x and y

x=+%286y-6%29%2F%283y%2B3%29+

x=+cross%286%292%28y-1%29%2Fcross%283%29%28y%2B1%29+

x=+2%28y-1%29%2F%28y%2B1%29+
x%28y%2B1%29=+2%28y-1%29+
xy%2Bx=+2y-2+

x%2B2=+2y-xy+

x%2B2=+%282-x%29y+

%28x%2B2%29%2F%282-x%29=y+

y=%28x%2B2%29%2F%282-x%29+
so, inverse is f%5E-1%28x%29=%28x%2B2%29%2F%282-x%29+