Functions Question 409
Question: Domain of definition of the function $ f(x)=\frac{3}{4-x^{2}}+{\log_{10}}(x^{3}-x) $ , is
[AIEEE 2003]
Options:
A) (1, 2)
B) $ (-1,\ 0)\cup (1,\ 2) $
C) $ (1,\ 2)\cup (2,\ \infty ) $
D) $ (-1,\ 0)\cup (1,\ 2)\cup (2,\ \infty ) $
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(x)=\frac{3}{4-x^{2}}+{\log_{10}}(x^{3}-x) $ . So, $ 4-x^{2}\ne 0 $
Þ $ x\ne \pm \sqrt{4} $ and $ x^{3}-x>0\Rightarrow x(x^{2}-1)>0 $
Þ $ x>0,,x>1 $ \ $ D=(-1,,0)\cup (1,,\infty )-{\sqrt{4}} $ i.e., $ D=(-1,,0)\cup (1,,2)\cup (2,,\infty ) $ .
BETA
