Question

What is the domain of the function f(x)=−4log2(x+3)−6 ? enter your answer in the box?

Answer 1

Try this solution:
1. according to the definition of logarithm
$log_ab=c \ =\ \textgreater \ \ a^c=b,$    where a∈(0;1)∪(1;+oo) and b>0.
2. The variable is only in b, using item 1. it is possible to write: x+3>0. 
⇒ x>-3.
Answer: D(f)=(-3;+oo).

Answer 2

To find the domain for $f(x)$, we first must find that domain of $\log2(x+3),$ as other integers do not influence the domain.

• For the domain $\to f(x), \ \ \ 2(x+3) > 0$ As a result,

                    $\to x + 3 > 0\\\\\to x>-3$

• As a result, any real numbers higher than -3 are in the domain of $f(x)$.
• According to the definition of logarithm

                   $\to \log_{a} b = c \geq a^c = b$, where $a \epsilon (0;1) U(1;+00)$ and$b>0$.

• Using item 1, the variable is only in b.
• It's feasible to write: $x+3>0, X-3.$

Therefore, the answer is "All real numbers < -3"

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