Find the Domain of f(x)=(|x|−2)/(|x|−3)

Find the Domain of \(f(x)=\dfrac{|x|-2}{|x|-3}\)

Question

Find the domain of the function

\[ f(x)=\frac{|x|-2}{|x|-3} \]

Given

\[ f(x)=\frac{|x|-2}{|x|-3} \]

For the function to be defined, the denominator must not be zero.

Therefore,

\[ |x|-3\ne0 \] \[ |x|\ne3 \]

Hence,

\[ x\ne3 \quad \text{and} \quad x\ne-3 \]

Thus all real numbers except \(-3\) and \(3\) belong to the domain.

\[ \boxed{\mathbb{R}\setminus\{-3,3\}} \]

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