What is the inverse function for f(x) = x / (x - 2)?

Solutions :

Given:

Function f(x) = x / (x - 2)

Now we have to find the inverse of the given function.

Step 1 :

Substitute function is equal to y.

f(x) = y

⇒  y = x / (x - 2)

Step 2 :

Now interchange x with y

⇒  x = y / (y - 2)

Step 3 :

Now solve the equation for y

⇒  x = y / (y - 2)

⇒  x (y - 2) = y

⇒  xy - 2x = y

⇒  xy - y = 2x

⇒  y(x - 1) = 2x

⇒  y = 2x / (x - 1)

Now, because we interchanged x with y 

y = f^-1(x) (inverse of the function)

f^-1(x) = 2x / (x - 1)

Therefore, the inverse of the function f(x) = x / (x - 2) is f^-1(x) = 2x / (x - 1).

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What is the inverse function for f(x) = x / (x - 2)?

Summary:

The inverse of the function f(x) = x / (x - 2) is f⁻¹(x) = 2x / (x - 1).