Understanding the Domain Restriction of the Function f(x) = log₂(-x) | A Math Explanation

f(x) = log₂(-x)

The function f(x) = log₂(-x) represents the logarithm of -x to the base 2

The function f(x) = log₂(-x) represents the logarithm of -x to the base 2. However, for this function to be defined, certain conditions should be met.

In this case, the input value -x must satisfy the following criteria:
1. -x > 0: The argument of the logarithm cannot be negative since the logarithm function is undefined for negative values. Therefore, x must be positive.

Considering that x is positive (x > 0), we can evaluate the function f(x) = log₂(-x) based on the logarithmic properties.

To find the value of f(x), we can use a logarithmic identity:
log(a) base b = log(a) / log(b)

Using this identity, we can rewrite f(x) as follows:
f(x) = log(-x) / log(2)

However, even with the positive x, log(-x) is still undefined since taking the logarithm of a non-positive value is not allowed. Consequently, the function f(x) = log₂(-x) is not defined for any positive x values.

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