Question

The domain of the function $f\left(x\right)={\log }_{(3+x)}(x^2-1)$ is

• A. $(-3,-1)\bigcup (1,\infty )$
• B. $[-3,-1)\bigcup [1,\infty )$
• C. $(-3,-2)\bigcup (-2,-1)\bigcup (1,\infty )$
• D. $[-3,-2)\bigcup (-2,-1)\bigcup [1,\infty ]$

Answer 1

The correct option is A $(-3,-1)\bigcup (1,\infty )$

$f\left(x\right)={\log }_{(3+x)}(x^2-1)$

$3+x>0$

$x^2-1>0$

$x>-3$

$x<-1$

$x<1$

So the domain of $f\left(x\right)$ is $(-3,-1)\bigcup (1,\infty )$