Question

The domain of logarithmic function f(x)=lnx
is x>0
. Which statement is true about its corresponding exponential function g(x)=ex
?(1 point)
Responses

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
.
Function g left parenthesis x right parenthesis has a range of y greater than 0 .

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
.

Answer 1

The function \( g(x) = e^x \) is the exponential function corresponding to the logarithmic function \( f(x) = \ln x \), which has a domain of \( x > 0 \).

For the function \( g(x) = e^x \):

- The domain of an exponential function is all real numbers, so \( g(x) \) has a domain of \( x \in (-\infty, \infty) \).
- The range of \( g(x) = e^x \) is \( y > 0 \) because the exponential function outputs positive values for all real inputs.

Thus, among the statements provided, the correct one is:

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