Functions Question 410
Question: Domain of definition of the function $ f(x)=\frac{3}{4-x^{2}}+{\log_{10}}(x^{3}-x), $ is
Options:
A) $ (-1,0)\cup (1,2)\cup (2,\infty ) $
B) $ (a,2) $
C) $ (-1,0)\cup (a,2) $
D) $ (1,2)\cup (2,\infty ) $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ f(x)=\frac{3}{4-x^{2}}+{\log_{10}}(x^{3}-x) $ $ 4-x^{2}\ne 0;x^{3}-x>0; $ $ x\ne \pm \sqrt{4} $ and $ -1<x<0 $ or $ 1<x<\infty $
$ \therefore D=(-1,0)\cup (1,\infty )-{\sqrt{4}} $ $ D=(-1,0)\cup (1,2)\cup (2,\infty ) $
BETA
