SOLUTION: I had this problem on a test. I found the inverse function, but I got stuck on the checking. Find the inverse function for f(x)=4x-2/3x. Check your answer.

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Question 62544: I had this problem on a test. I found the inverse function, but I got stuck on the checking.
Find the inverse function for f(x)=4x-2/3x. Check your answer.
Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse function for f(x)=4x-2/3x. Check your answer.
Let f(x)=y
y=%284x-2%29%2F3x
Change the y's to x's and the x's to y's.
x=%284y-2%29%2F3y Solve for y.
3y%28x%29=%283y%29%284y-2%29%2F3y
3xy=4y-2
3xy-4y=-4y%2B4y-2
3xy-4y=-2
y%283x-4%29=-2
y%283x-4%29%2F%283x-4%29=-2%2F%283x-4%29
y=-2%2F%283x-4%29
let y=f^-1(x)
f^-1(x)=-2%2F%283x-4%29
To check take the f(f^-1(x)) and f^-1(f(x)) if they equal x, then they are inverses. [This is taking the composite functions. You substitute the functions into each other and simplify. If this is completely foreign to you let me know and I'll explain this more thoroughly.]
f(f^-1(x))=%284%28-2%2F%283x-4%29%29-2%29%2F%283%28-2%2F%283x-4%29%29%29
=%28-8%2F%283x-4%29-2%29%2F%28-6%2F%283x-4%29%29
=%283x-4%29%28-8%2F%283x-4%29-2%29%2F%28%283x-4%29%28-6%2F%283x-4%29%29%29
%28-8-2%283x-4%29%29%2F-6
%28-8-6x%2B8%29%2F-6
-6x%2F-6
x Yes!!!! This means that they are very likely inverses, but to be thorough, check f^-1(f(x))
f^-1(f(x))=-2%2F%283%28%284x-2%29%2F3x%29-4%29
=-2%2F%28%284x-2%29%2Fx-4%29
=-2x%2F%28x%284x-2%29%2Fx-4%29%29
=-2x%2F%284x-2-4x%29
=-2x%2F-2
=x Yes!!! This means that we're right!!!!
Happy Calculating!!!