what are the domain and range of (f(x)=log(x + 6)-4)?\no domain: (x>-6); range: (y > 4)\no domain: (x>-6)…

Explanation:

Step1: Find the domain

For the logarithmic function $y = \log(u)$, the argument $u$ must be positive. Here $u=x + 6$, so we set $x+6>0$. Solving for $x$ gives $x>-6$.

Step2: Find the range

The range of the basic logarithmic function $y=\log(x)$ is all real numbers. The function $f(x)=\log(x + 6)-4$ is a vertical - shift of the basic logarithmic function. Shifting a function vertically does not change its range. So the range of $f(x)$ is all real numbers.

Answer:

domain: $x > -6$; range: all real numbers