question_answer

If \[f(x)=\frac{1}{\sqrt{(x+1)({{e}^{x}}-1)(x-4)(x+5)(x-6)}}\]Then the domain of f(x) is

A) \[(-\infty ,-5)\cup (-1,4)\cup (6,\infty )\]

B) \[(-\infty ,-5)\cup (-1,0)\cup (0,4)\cup (6,\infty )\]

C) \[(-5,-1)\cup (0,4)\cup (6,\infty )\]

D) None of these

Correct Answer: C

Solution :

[c] \[f(x)=\frac{1}{\sqrt{(x+1)({{e}^{x}}-1)(x-4)(x+5)(x-6)}}\] \[f(x)\] is defined is \[(x+1)({{e}^{x}}-1)(x-4)(x+5)(x-8)\] >0 Hence, \[x\in (-5,-1)\cup (0,4)\cup (6,\infty )\]