Question #6451898Fill in the Blank
Algebra-2
Question
The domain of the function is all real numbers such that x ______.
Answer & Analysis
Analysis
Question Analysis
This question involves finding the domain of a logarithmic function with a linear expression inside the logarithm.
The main focus is on the rule that the argument (input) of a logarithm must be positive.
Key Concept Explanation
The domain of a function is the set of all valid input values (x-values) for which the function is defined. For logarithmic functions:
is only defined if (the argument must be positive).
If is an expression (e.g., ), solve the inequality to find the domain.
Step-by-Step Solution
1. Identify the argument of : .
2. Set up the inequality for the domain: .
3. Solve for
This question involves finding the domain of a logarithmic function with a linear expression inside the logarithm.
The main focus is on the rule that the argument (input) of a logarithm must be positive.
Key Concept Explanation
The domain of a function is the set of all valid input values (x-values) for which the function is defined. For logarithmic functions:
is only defined if (the argument must be positive).
If is an expression (e.g., ), solve the inequality to find the domain.
Step-by-Step Solution
1. Identify the argument of : .
2. Set up the inequality for the domain: .
3. Solve for
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