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Domain of f(x)=\frac{1}{\left|x^{2}-4\right|}  is

Option: 1

R


Option: 2

R-\left \{ 2 \right \}


Option: 3

R-\left \{ -2,2 \right \}


Option: 4

None of these


Answers (1)

best_answer

As the mod term is in the denominator, so it cannot equal 0.

So,

\begin{aligned} &\left|x^{2}-4\right| \neq 0 \\ &\Rightarrow x^{2}-4 \neq 0 \\ &\Rightarrow(x+2)(x-2) \neq 0 \\ &\Rightarrow x \neq 2, x \neq-2 . \end{aligned}

So, Domain is R-\left \{ -2,2 \right \}

Posted by

Ajit Kumar Dubey

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