Problem:
For all real numbers x, except x = 0 and x = 1, function f is defined by f(x/(x-1)) = 1/x. Explain in detail.

Solution:
To understand the given function and its domain, let's break down the problem into smaller parts and analyze them step by step.

Understanding the Function and its Domain:
The given function is defined as f(x/(x-1)) = 1/x. Here, x can take any real value except 0 and 1. Let's understand the function and its domain in detail.

Function Definition:
The function f(x/(x-1)) = 1/x can be read as "f of x divided by (x-1) is equal to 1/x." It means that when we input a value of x into the function, we divide it by (x-1) and the result is equal to 1 divided by x.

Domain Restrictions:
The domain of the function is the set of all possible values for which the function is defined. In this case, x cannot be equal to 0 or 1. Therefore, the domain of the function is all real numbers except 0 and 1.

Simplifying the Function:
To better understand the function, let's simplify it using algebraic manipulation.

Step 1: Substitute x/(x-1) with a variable, let's say y.
y = x/(x-1)
Step 2: Rewrite the function in terms of y.
f(y) = 1/(y+1)

Understanding the Simplified Function:
After simplifying the function, we have f(y) = 1/(y+1). Here, y represents x/(x-1). Let's analyze the simplified function in detail.

Function Definition:
The simplified function f(y) = 1/(y+1) can be read as "f of y is equal to 1 divided by (y+1)." It means that when we input a value of y into the function, we divide 1 by (y+1) to get the result.

Domain Restrictions:
Since y represents x/(x-1), we need to consider the domain restrictions for y as well. As x cannot be equal to 0 or 1, y cannot take the value of 0. Therefore, the domain of the simplified function is all real numbers except 0.

Conclusion:
In conclusion, the function f(x/(x-1)) = 1/x is defined for all real numbers except 0 and 1. The simplified form of the function is f(y) = 1/(y+1), where y represents x/(x-1). The domain of the simplified function is all real numbers except 0.