Answer:
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: