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

Function g(x)
has a range of y≤0
.

Answer 1

The correct statement about the corresponding exponential function \( g(x) = e^x \) is:

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

Explanation:

• The domain of the exponential function \( g(x) = e^x \) is all real numbers, \( x \in (-\infty, \infty) \), but none of the options provided mention that.
• The range of the exponential function is \( y > 0 \) since \( e^x \) is always positive for any real number \( x \).