Question
The domain of logarithmic function f(x) = 1n x is x > 0. Which statement is true about its corresponding function g(x) = e^x
The function g(x) has a domain of x > 0
The function g(x) has a range of y > 0
The function g(x) has a domain of x </ 0
Function g(x) has a range y </0
The function g(x) has a domain of x > 0
The function g(x) has a range of y > 0
The function g(x) has a domain of x </ 0
Function g(x) has a range y </0
Answers
GPT-4o mini
Let's analyze the function \( g(x) = e^x \):
1. **Domain of \( g(x) \)**:
- The function \( g(x) = e^x \) is defined for all real numbers \( x \). Therefore, its domain is \( x \in (-\infty, \infty) \).
2. **Range of \( g(x) \)**:
- The output of \( g(x) = e^x \) is always positive because the exponential function always returns positive values regardless of whether \( x \) is positive or negative. Thus, the range of \( g(x) \) is \( y > 0 \).
Based on this analysis, the correct statement is:
**The function g(x) has a range of y > 0.**
1. **Domain of \( g(x) \)**:
- The function \( g(x) = e^x \) is defined for all real numbers \( x \). Therefore, its domain is \( x \in (-\infty, \infty) \).
2. **Range of \( g(x) \)**:
- The output of \( g(x) = e^x \) is always positive because the exponential function always returns positive values regardless of whether \( x \) is positive or negative. Thus, the range of \( g(x) \) is \( y > 0 \).
Based on this analysis, the correct statement is:
**The function g(x) has a range of y > 0.**