State the domain and range of the function.
-$$f ( x ) = \frac { 5 } { 9 + e ^ { x } }$$
A) domain: $( - \infty , \infty )$; range: $\left( 0 , \frac { 5 } { 9 } \right)$
B) domain: $( 0 , \infty )$; range: $( 0 , \infty )$
C) domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$
D) domain: $( - \infty , \infty )$; range: $( 0,9 )$

Question

Quizplus · Accepted Answer

The domain of $f(x) = \frac{5}{9 + e^x}$ is all real numbers because the exponential function $e^x$ is defined for all real numbers, and adding 9 to it will never make the denominator zero. The range is $\left(0, \frac{5}{9}\right)$ because $e^x$ is always positive, making the denominator always greater than 9, so the fraction is always positive but less than $\frac{5}{9}$.

State the Domain and Range of the Function f(x)=59+exf ( x ) = \frac { 5 } { 9 + e ^ { x } }f(x)=9+ex5​

State the Domain and Range of the Function $f ( x ) = \frac { 5 } { 9 + e ^ { x } }$