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 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
.

1 answer

The logarithmic function \( f(x) = \ln x \) has a domain of \( x > 0 \), which means it is defined only for positive values of \( x \). The corresponding exponential function is \( g(x) = e^x \).

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

  • Domain: The exponential function is defined for all real numbers, so it's domain is \( x \in (-\infty, \infty) \).
  • Range: The output of \( e^x \) is always positive, hence the range is \( y > 0 \).

Considering the given statements, the true statement about the exponential function \( g(x) = e^x \) is:

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