Question

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

Answer 1

$f(x)=\log(x+6)-4\\\\\text{The domain:}\\x+6 \ \textgreater \ 0\to x \ \textgreater \ -6\to x\in(6;\ \infty)\\\\\text{the range of}\ y=\log x\ \text{is}\ \mathbb{R}\\\text{and the range of}\ y=\log(x+6)\ \text{is}\ \mathbb{R}\\\text{and the range of}\ f(x)=\log(x+6)-4\ \text{is}\ \mathbb{R}$