The domain of logarithmic function f(x)=lnx

Question

is x>0
. Which statement is true about its corresponding exponential function g(x)=ex
?(1 point)
Responses

Function g(x)
has a range of y≤0
.
Function g left parenthesis x right parenthesis has a range of y less-than-or-equal-to 0 .

Function g(x)
has a domain of x>0
.
Function g left parenthesis x right parenthesis has a domain of x greater than 0 .

Function g(x)
has a domain of x≤0
.
Function g left parenthesis x right parenthesis has a domain of x less-than-or-equal-to 0 .

Function g(x)
has a range of y>0
.

Answer 1

For the exponential function \( g(x) = e^x \), the properties are as follows:

1. The domain of \( g(x) = e^x \) is all real numbers, \( (-\infty, \infty) \).
2. The range of \( g(x) = e^x \) is \( y > 0 \) because the output of an exponential function is always positive.

Given the options, the true statement about the exponential function \( g(x) = e^x \) corresponding to the logarithmic function \( f(x) = \ln(x) \) is:

Function \( g(x) \) has a range of \( y > 0 \).