Question

what are the domain and range of the logarithmic function \\(f(x) = \log_7 x\\)? use the inverse function to justify your answers.

check each item below that you included in your response.

• the domain of \\(f\\) is \\(x > 0\\).
• the range of \\(f\\) is all real numbers.
• the domain of the inverse function is all real numbers.
• the range of the inverse function is \\(y > 0\\).
• the domain of \\(f\\) is the same as the range of the inverse function.
• the range of \\(f\\) is the same as the domain of the inverse function.

Explanation:

Find the inverse function

$$
LATEXBLOCK0
$$

Determine domain and range of the inverse function

$$
LATEXBLOCK1
$$

Map to the original function

$$
LATEXBLOCK2
$$

Answer:

• The domain of \(f\) is \(x > 0\). (Correct answer)
• The range of \(f\) is all real numbers. (Correct answer)
• The domain of the inverse function is all real numbers. (Correct answer)
• The range of the inverse function is \(y > 0\). (Correct answer)
• The domain of \(f\) is the same as the range of the inverse function. (Correct answer)
• The range of \(f\) is the same as the domain of the inverse function. (Correct answer)