Question

What are the domain and Range of f(x)=log(x+6)-4

Answer 1

The function $g(x)=\log x$ has domain $(0,\infty)$ and range $(-\infty, \infty )$.

The function $f(x)=\log(x+6)-4$ is obtained from the function $g(x)$ by translating 6 units left and 4 units down.

So, the domain of $f(x)$ is $(-6,\infty)$ and range is $(-\infty, \infty )$.