I posted a problem earlier and made a mistake the question is what is the domain and range of f(x)= log subscript 3 (1-x)? Sorry!

The answer is the same. The domain and range will be the same as if it were log base 40.

No problem! Let's find the domain and range of the function:

The domain of a logarithmic function is the set of all real numbers for which the argument (the expression inside the logarithm) is greater than zero. In this case, the argument is 1-x. So, 1-x > 0.

To find the domain, solve the inequality:

1 - x > 0

Adding x to both sides:

1 > x

Therefore, the domain of the function is x < 1, meaning any real number less than 1.

The range of a logarithmic function is the set of all possible output values. In this case, the base of the logarithm is 3. So, we can examine the behavior of y = log base 3 x to determine the range.

As x approaches positive infinity, y approaches positive infinity. As x approaches 0 (from the right), y decreases towards negative infinity. So, the range of the function is all real numbers.

To summarize:
- The domain of f(x) = log₃(1-x) is x < 1.
- The range of f(x) = log₃(1-x) is all real numbers.