Question

what are the domain and range of \\(f(x) = \log x - 5\\)?

domain: \\(x > 0\\); range: all real numbers
domain: \\(x < 0\\); range: all real numbers
domain: \\(x > 5\\); range: \\(y > 5\\)
domain: \\(x > 5\\); range: \\(y > -5\\)

Explanation:

Determine the domain restriction of the logarithmic function

$$ x > 0 $$

Determine the range of the logarithmic function

$$ \text{range: all real numbers} $$

Answer:

• domain: \(x > 0\); range: all real numbers (Correct answer)
• domain: \(x < 0\); range: all real numbers
• domain: \(x > 5\); range: \(y > 5\)
• domain: \(x > 5\); range: \(y > -5\)