Question
The range of exponential function function f(x)=e^x
is y>0
. Which statement is true about its corresponding logarithmic function g(x)=ln x
?(1 point)
Responses
Function g(x)
has a domain of x>0
.
Function g of x has a domain of x is greater than 0.
Function g(x)
has a range of y>0
.
Function g of x has a range of y is greater than 0.
Function g(x)
has a domain of x≤0
.
Function g of x has a domain of x is less than or equal to 0.
Function g(x)
has a range of y≤0
.
Function g of x has a range of y is less than or equal to 0.
is y>0
. Which statement is true about its corresponding logarithmic function g(x)=ln x
?(1 point)
Responses
Function g(x)
has a domain of x>0
.
Function g of x has a domain of x is greater than 0.
Function g(x)
has a range of y>0
.
Function g of x has a range of y is greater than 0.
Function g(x)
has a domain of x≤0
.
Function g of x has a domain of x is less than or equal to 0.
Function g(x)
has a range of y≤0
.
Function g of x has a range of y is less than or equal to 0.
Answers
GPT-4o mini
The correct statement regarding the logarithmic function \( g(x) = \ln x \) in relation to its domain and range is:
**Function g(x) has a domain of \( x > 0 \).**
This is because the natural logarithm \( \ln x \) is defined only for positive values of \( x \). Therefore, the domain of \( g(x) \) is indeed \( x > 0 \).
The range of \( g(x) \) is all real numbers, which would be \( y \in (-\infty, +\infty) \). Thus, the other options related to its range are not true.
**Function g(x) has a domain of \( x > 0 \).**
This is because the natural logarithm \( \ln x \) is defined only for positive values of \( x \). Therefore, the domain of \( g(x) \) is indeed \( x > 0 \).
The range of \( g(x) \) is all real numbers, which would be \( y \in (-\infty, +\infty) \). Thus, the other options related to its range are not true.