Question

Find the domain of $h\left(x\right)=\frac{(3x-6)}{\sqrt{(x^2+2x-8)}}$

• A. $(-\infty ,-5)\cup (3,+\infty )$
• B. $(-\infty ,-1)\cup (7,+\infty )$
• C. $(-\infty ,-4)\cup (2,+\infty )$
• D. $(-\infty ,1)\cup (9,+\infty )$

Answer 1

The correct option is C $(-\infty ,-4)\cup (2,+\infty )$

Domain of a function are the values which u can plug into a function so that u get a viable answer (the answer isn't infinity or a sqrt of a negative number etc..)
in this function u can plug in all values of $x$ except when $\sqrt{(x^2+2x-8)}=0$ that is $x^2+2x-8=0$

$\Rightarrow x^2-2x-4x-8=0$

$\Rightarrow x(x-2)+4(x-2)=0$ that is

$\Rightarrow (x-2)=0$ and $(x+4)=0$

$\Rightarrow x=2$ and $x=-4$

because when we put $x=-4$ and $x=2$, the denominator of the given function will be $0$, which is not defined (infinity). so domain is

$(-\infty ,-4)\cup (2,+\infty )$