what are the domain and range of the function (f(x)=-log(5 - x)+9)?\no domain: (x < 5)\nrange: (ygeq9)\no…

Explanation:

Step1: Find the domain

For the logarithm $\log(5 - x)$ to be well - defined, the argument must be positive. So we set up the inequality $5−x>0$. $5−x>0\Rightarrow -x>- 5\Rightarrow x < 5$.

Step2: Find the range

The range of the basic logarithmic function $y = \log(u)$ is $(-\infty,\infty)$. Here, $y=-\log(5 - x)+9$. Since the range of $\log(5 - x)$ is $(-\infty,\infty)$, when we multiply it by $- 1$ and then add $9$, the range of $y =-\log(5 - x)+9$ is also $(-\infty,\infty)$.

Answer:

domain: $x < 5$ range: $(-\infty,\infty)$