SOLUTION: The function f(x)=7x+2/x-3, x≠3, is one-to-one. Find an equation for f^-1(x), the inverse function.

Algebra ->  Functions -> SOLUTION: The function f(x)=7x+2/x-3, x≠3, is one-to-one. Find an equation for f^-1(x), the inverse function.      Log On


   

Question 1160895: The function f(x)=7x+2/x-3, x≠3, is one-to-one. Find an equation for f^-1(x), the inverse function.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The function f(x)=7x+2/x-3, x≠3, is one-to-one.
Find an equation for f^-1(x), the inverse function.
:
y = %287x%2B2%29%2F%28x-3%29
swap x and y and solve for y
x = %287y%2B2%29%2F%28y-3%29
multiply both sides by (y-3), cancels out the left side
x(y-3) = 7y + 2
distribute x
xy - 3x = 7y + 2
add 3x to both sides, subtract 7y from both sides
xy - 7y = 3x + 2
factor out y
y(x-7) = 3x + 2
divide both sides by (x-7)
y = %283x%2B2%29%2F%28x-7%29 is the inverse function