Functions
Domain
MMTS_Full_Test_12
Grade 12
Question:
If the domain of the function $f(x)=\dfrac{\sqrt{x^2-16}}{x^2-4}+\log_{10}(x^2+3x-10)$ is $(-\infty,p)\cup[q,\infty)$, then $p^2+q=$
Step-by-Step Solution
Key Concept: $x^2-16\ge 0$ and $x^2-4\ne 0$ and $x^2+3x-10>0$
$|x|\ge 4$, $x\ne\pm 2$, $(x+5)(x-2)>0\Rightarrow x<-5$ or $x>2$. Domain: $(-\infty,-5)\cup[4,\infty)$ (excluding $x=-2$, but $-2>-5$: irrelevant). $p=-5,q=4$. $p^2+q=29$.
Correct Answer: 2