Questions: Find the domain and range of y=log₂(5-4x). The domain is: The range is:

Solution Steps

To find the domain of the function \( y = \log_{2}(5 - 4x) \), we need to determine the values of \( x \) for which the argument of the logarithm, \( 5 - 4x \), is positive. For the range, we consider the possible values of \( y \) that result from the domain.

To find the domain of the function \( y = \log_{2}(5 - 4x) \), we need the argument of the logarithm, \( 5 - 4x \), to be positive. Therefore, we solve the inequality:

\[ 5 - 4x > 0 \]

Solving for \( x \), we get:

\[ 5 > 4x \quad \Rightarrow \quad x < \frac{5}{4} \]

Thus, the domain of the function is:

\[ x \in \left(-\infty, \frac{5}{4}\right) \]

The range of a logarithmic function is all real numbers, as the logarithm can take any real value. Therefore, the range of \( y = \log_{2}(5 - 4x) \) is:

\[ y \in (-\infty, \infty) \]

Final Answer