Question
The exponential function f(x)=19x
has a domain of all real numbers. What conclusion can you draw about the logarithmic function g(x)=log19x
?(1 point)
Responses
The domain of g(x)=log19x
cannot be determined.
The domain of g left parenthesis x right parenthesis equals logarithm subscript 19 baseline x cannot be determined.
The range of g(x)=log19x
is all real numbers.
The range of g left parenthesis x right parenthesis equals logarithm subscript 19 baseline x is all real numbers.
The domain of g(x)=log19x
is all real numbers.
The domain of g left parenthesis x right parenthesis equals logarithm subscript 19 baseline x is all real numbers.
The range of g(x)=log19x
cannot be determined.
has a domain of all real numbers. What conclusion can you draw about the logarithmic function g(x)=log19x
?(1 point)
Responses
The domain of g(x)=log19x
cannot be determined.
The domain of g left parenthesis x right parenthesis equals logarithm subscript 19 baseline x cannot be determined.
The range of g(x)=log19x
is all real numbers.
The range of g left parenthesis x right parenthesis equals logarithm subscript 19 baseline x is all real numbers.
The domain of g(x)=log19x
is all real numbers.
The domain of g left parenthesis x right parenthesis equals logarithm subscript 19 baseline x is all real numbers.
The range of g(x)=log19x
cannot be determined.
Answers
Answered by
GPT-4o mini
To analyze the logarithmic function \( g(x) = \log_{19}(x) \), we need to consider its domain and range.
1. **Domain of \( g(x) = \log_{19}(x) \)**: The logarithmic function is defined only for positive arguments. Therefore, the domain of \( g(x) \) is \( x > 0 \), which means the domain is \( (0, \infty) \) in interval notation.
2. **Range of \( g(x) = \log_{19}(x) \)**: The logarithmic function can take any real number as its output. Therefore, the range of \( g(x) \) is all real numbers, which we can express as \( (-\infty, \infty) \).
Based on this understanding, the relevant conclusion we can draw from the provided options is:
- The range of \( g(x) = \log_{19}(x) \) is all real numbers.
So the best response is:
- The range of \( g(x)=\log_{19}(x) \) is all real numbers.
1. **Domain of \( g(x) = \log_{19}(x) \)**: The logarithmic function is defined only for positive arguments. Therefore, the domain of \( g(x) \) is \( x > 0 \), which means the domain is \( (0, \infty) \) in interval notation.
2. **Range of \( g(x) = \log_{19}(x) \)**: The logarithmic function can take any real number as its output. Therefore, the range of \( g(x) \) is all real numbers, which we can express as \( (-\infty, \infty) \).
Based on this understanding, the relevant conclusion we can draw from the provided options is:
- The range of \( g(x) = \log_{19}(x) \) is all real numbers.
So the best response is:
- The range of \( g(x)=\log_{19}(x) \) is all real numbers.