Question

Find the inverse of the function.

f-¹(x) =
+
f(x) =
1
x - 2
X # 2
, X = 0

Answer 1

The given function is:

f(x) = 1/(x - 2), x ≠ 2

0, x = 2

To find the inverse of the function, we need to solve for x in terms of f(x).

Let y = f(x)

Case 1: When y = 0

If y = 0, then x = 2 as per the definition of the function.

Case 2: When y ≠ 0

y = 1/(x - 2)

1/y = x - 2

x = 1/y + 2

So, the inverse function is:

f-¹(x) = 2, x = 0

1/(x - 2), x ≠ 0 and x ≠ 2

Explanation: