Question

Identify the domain of the function $f\left(x\right)=\frac{1}{\sqrt{x^2-16}}$.

• A. All the real numbers
• B. $x<-4$ or $x>4$
• C. $x\ge 4$
• D. $x>8$
• E. $x<-8$ or $x>8$

Answer 1

The correct option is B $x<-4$ or $x>4$

Given function is $f\left(x\right)=\frac{1}{\sqrt{x^2-16}}$

The domain of function will be $x^2-16\ge 0$
$(x-4)(x+4)\ge 0$ , which gives $x<-4$ and $x>4$