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The inverse function of f(x) = x / (x - 2) is found by first swapping x and y to get x = y / (y - 2), then simplifying to solve for y. After some algebraic manipulations, it is found that the inverse function is f^-1(x) = 2x / (x - 1).
To find the inverse function of a function, we swap x and y and then solve for y. Given the function f(x) = x / (x - 2), this becomes y = x / (x - 2). Now, to find the inverse, we swap 'x' and 'y' so that it becomes x = y / (y - 2). Now our goal is to solve for y.
Finding the inverse involves some algebraic manipulations. First, cross multiply to remove the fraction: x(y - 2) = y. Simplify this to xy - 2x = y. Move 'y' to the other side and that gives you xy - y = 2x.
Next, 'y' appears on both terms on the left on the equation so you can factor out 'y': y(x - 1) = 2x. You can then solve for y by dividing both sides by (x - 1). This gives you the inverse function: y = 2x / (x - 1).
Therefore, the inverse of function f(x) is f^-1(x) = 2x / (x - 1).
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