To find the inverse of function f(x), we first need to replace f(x) with y. Thus we have y = 4/x + 6.
Next, we swap x and y as the first step to finding the inverse. This gives us x = 4/y + 6.
Our goal is to get the equation in terms of y.
We start by subtracting 6 from both sides, obtaining x - 6 = 4/y.
To make y the subject of our equation, we multiply both sides by y, this gives us y(x - 6) = 4.
Finally, we divide both sides by (x-6) so that y is isolated on one side: y = 4 / (x - 6).
So, the inverse of the function f(x)=4/x + 6 is y = 4 / (x - 6).