Question
The domain of logarithmic function f(x)=ln x
is x>0
. Which statement is true about its corresponding exponential function g(x)=e^x
?(1 point)
Responses
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
.
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
.
Function g left parenthesis x right parenthesis has a domain of x less-than-or-equal-to 0 .
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is x>0
. Which statement is true about its corresponding exponential function g(x)=e^x
?(1 point)
Responses
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
.
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
.
Function g left parenthesis x right parenthesis has a domain of x less-than-or-equal-to 0 .
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Answers
GPT-4o mini
For the function \( g(x) = e^x \):
1. The domain refers to all the possible input values (x-values) for which the function is defined. In the case of \( g(x) = e^x \), it is defined for all real numbers. So, the domain is \( (-\infty, \infty) \), which can also be represented as \( x \in \mathbb{R} \).
2. The range refers to all possible output values (y-values) the function can produce. For \( g(x) = e^x \), the output is always positive because the exponential function never reaches zero and thus, the range is \( (0, \infty) \), which can be written as \( y > 0 \).
Given these points, the true statement about the function \( g(x) \) is:
**Function g(x) has a range of y > 0.**
The corresponding option could also be written as "Function \( g(x) \) has a range of \( y \) greater than 0." Both statements convey the same meaning.
1. The domain refers to all the possible input values (x-values) for which the function is defined. In the case of \( g(x) = e^x \), it is defined for all real numbers. So, the domain is \( (-\infty, \infty) \), which can also be represented as \( x \in \mathbb{R} \).
2. The range refers to all possible output values (y-values) the function can produce. For \( g(x) = e^x \), the output is always positive because the exponential function never reaches zero and thus, the range is \( (0, \infty) \), which can be written as \( y > 0 \).
Given these points, the true statement about the function \( g(x) \) is:
**Function g(x) has a range of y > 0.**
The corresponding option could also be written as "Function \( g(x) \) has a range of \( y \) greater than 0." Both statements convey the same meaning.