The inverse of f(x) is (6x + 2)/x.
What is an inverse function?
The inverse function is defined as a function obtained by reversing the given function.
Given that f(x) = 2/(x-6)
To determine the inverse of a function, all you have to do is switch where x and y are and resolve for y.
So after switching x and y,
f(x) = y = 2/(x-6)
becomes
x = 2/(y - 6)
Now, we solve for y regularly.
f(x) = y = 2/(x-6)
Solve for y :
⇒ x(y - 6) =2
⇒ xy - 6x = 2
⇒ y = (6x + 2)/x
Therefore the inverse of f(x) is (6x + 2)/x
Learn more about inverse function here:
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